@OP: can you tell us if the procedure worked?
I think knightdk's, vlamer and my own post should have been sufficient to solve your problem, so it might be nice to give some feedback in case somebody else ever searches for this problem... That way they'll know the problem can be fixed with the info given in this thread

She doesn't really care as long as I don't risk our livesavings when buying bitcoins

Okay guys, there are a couple things i wish to rectify here... Also, OP, i've tried to answer your question at the bottom of this post:

Disclaimer: i have bitcoind running on a linux server, i haven't updated for a while, so if something substantially changed in the last couple of versions, this post might be inaccurate. Also, i usually run bitcoind, not bitcoin-qt (the gui). They use the same blockchain, so everything for bitcoind should be more or less the same for bitcoin-qt:

1) it can take days/weeks to synchronise bitcoin core (but defenately not hours, unless you have access to a 64 core XEON server with 256 Gb ram and RAID5 SSD disks on a really fast network). It depends on many factors: your cpu, the speed of your disks, your memory, your internet connection. The last time i synced the blockchain, it took me over 2 days on a server with 16 Gb ram, 15k rpm disks, 4 XEON processors and a really fast network. You can check how far along the synchronisation is by either looking at the bitcoin-qt gui, or looking in the debug.log (since i run bitcoind i only know/can verify to look into the debug.log, but if i remember correctly, the gui also indicated how much of the blockchain was already synced... I did not verify this tough).

2) On my server, i have a dedicated bitcoin-user, the partition in which the blockchain resides is 90+ Gb, and contains allmost only block data. It is allmost full.

OP: before you do ANYTHING, ALWAYS backup your wallet.dat!!! in linux you can find this file in ~/.bitcoin/wallet.dat if you did a default installation, in windows it's somewhere else, you can either use google, or use your windows searchfunction to find it.


OP: to answer your question, a very little lecture... I've tried to keep the explanation newbie-friendly and might have omitted some details, so you cannot use this explanation as a fact, more as a tool to explain what is happening:
A wallet is a piece of software that has a specific task: maintaining your private keys. A private key is the basis of bitcoin. It is (as the name says) a piece of text that you NEED to keep PRIVATE. It is used to controll your bitcoins. Your address is derived from this private key, but can be shared. If somebody gets your private key, he controlls your address and can send your coins to himself!!! I'm tired, and for this little lecture it's a bit to much to give the technical explanation of how this works exactly.
Bitcoin-qt (the client you installed) manages your private keys. It is designed to generate a new private key (and a new address) each time you send coins (to collect your change). It also generates a new private key each time you request coins. Your wallet might manage hundreds of private keys!!! Electrum is a different wallet, it also manages private keys, the big difference is that electrum only download (very small) headers. It uses a central server to get all other information, but keeps your private keys safe on your pc (so the central server cannot get its hands on your keys => it's pretty safe to use electrum).

Now, if you're 100% sure you have only used your wallet to RECEIVE this ONE incoming transaction, and you HAVE NOT used your wallet to send coins, ask more than 1 transaction,... you can try to export your private key for this address.
I could try to explain how to do this, but people have already made this explanation before me: http://docs.bitshares.org/muse/migration/howto-exporting-wallet-clients.html (look for the explanation of bitcoin qt).

Importing a private key into electrum is pretty easy: just open electrum... If it's the first time you open it, it'll show a wizard, otherwise go to file=>new/restore => restore a wallet or import keys => paste your private key...

If you don't see all your funds in electrum, there must have been more than one address/private key in use in bitcoin-qt, and you can either export these other private keys to, or just wait it out using bitcoin-qt.

I must say i'm rather proud of a new user chosing bitcoin. You made the right decission of chosing a desktop wallet, but you were unlucky because you did this in a hurry and chose a wallet that required a lot of time to synchronise (altough it's a great wallet, it's the basic wallet and it's safe and has a lot of functionality). I hope you stick around the bitcoin community after this first try, it's a good community and a good idear, you just have to give it a chance

Disclaimer2: it's late in my country, i'm tired and going to bed... It might be wise to wait untill a second longtime member verifies my steps before actually doing them!

There are a couple ways to export keys and import them into an spv wallet (these ones do not need to sync the full blockchain). However, for a new user this might be fairly complex.

If there isn't any urgency, it might be best to just keep your PC and bitcoin core running until its synced tough.

If its urgent, let us know and we'll try to show you how to export/import

It's not that hard to do actually.. I've created a couple double spends when my transactions got stuck when I added a to low fee.
I'm pretty sure that I can create a double spend in a matter of minutes when I have had time to prepare beforehand.

Ramnode has never steered me wrong... They used to accept bitcoins as a payment option, but i don't know if they still do tough.

<Bump> (this post will be removed and re-added after at least 24 hours have passed)

well... bitcoin core keeps track of several private keys, it generates new addresses as change addresses every time you send coins, and new addresses to receive coins. One wallet can contain hundreds of addresses/private keys... If you want to go from bitcoin core to blockchain.info (a move i would strongly discourage), you'd need to export your private keys from core.
In order to do this, you can follow the first part of this tutorial: https://github.com/OmniLayer/omniwallet/wiki/Exporting-a-private-key-from-Bitcoin-QT-Bitcoin-core-and-Importing-to-Omniwallet.org (you'll need to repeat this for every address containing funds!!!)

Afterwards, you can import your private key(s) into blockchain.info: https://en.bitcoin.it/wiki/How_to_import_private_keys#Using_Blockchain.info
A second tutorial: https://www.youtube.com/watch?v=obvLpYOVqUs (you'll need to import all private keys you exported in the first step)


BEFORE you do ANYTHING, backup your wallet.dat to a SECURE location
and always realise you went from a relatively secure system to an online wallet, handing over your private keys to an untrusted server trough an SSL connection you cannot 100% trust...

Indeed... If i get a single input of 1000BTC (~$450.000) from a stranger, and i use this single input to create one output, the transaction size will probably be really small (one input -> one output = not a lot of "text"). The fee would probably be a couple cents.

estimated size: 180 * 1 + 34*1 + 10 = 224 bytes
fee to get included in a block really fast: 30 satoshi's per byte => 224 * 30 = 0.00006720 BTC

If i get 1000 inputs of 1 bitcoin from a stranger, and i use it to create one output, the transaction size will be much larger (you can use this post to do an estimation: https://bitcointalk.org/index.php?topic=124302.0). The fee would be a lot more.

estimated size: 180 * 1000 + 34*1 + 10 = 180044 bytes
fee to get included in a block really fast: 30 satoshi's per byte => 180044 * 30 = 0.05401320 BTC

you can use this page to see how much fee per byte is advisable, and how long it will take ON AVERAGE for such a fee to be included in a block:
https://bitcoinfees.21.co/

EDIT: estimations done in red
As you can see by my estimations, both transactions sent 1000BTC, but the first transaction only included a 3 dollarcent fee, while the second transaction included a 25 dollar fee... Both should get the same priority by the miners because they both payed 30 satoshi's per byte... The only difference was the ammount of inputs. Translated to your situation => if you have a lot of really small inputs, the percentage of the fee you'll need to pay rises really high.

EDIT2: also not this fee will stay the same if you create a single output of 1000 1BTC inputs, or from 1000 0.1BTC inputs or from 1000 0.0001BTC inputs. the size of the output will offcourse differ, but the fee stays the same.

Sure, i'll try to give a not-to-theoretical version, so it's easyer to read:

PUBLIC NOTE: this is an extremely simplified version, i know it's missing some key aspects, but i wanted to convey the general idear behind fees and transaction sizes!!! Don't take this text and use it as a correct theory.

The bitcoin blockchain is a public ledger (everybody can download and verify it)... It's a database containing each and every bitcoin transaction ever made. In order to generate a transaction you need to define which inputs you want to use to create an output. You basically need to create a text saying (well, actually, your wallet will create this "text" for you): i'm using input A and input B to create output C, output D and output F. offcourse it isn't litterally this text, it's basically a code and there's a lot of hashing and signing going on, making sure you can only spend inputs you controll (inputs that were sent to an address you hold the private key to... but this is managed by your wallet, so you don't have to worry about this either).

As you can see, the more inputs and outputs, the longer the transaction "text" will be. This results in the fact that the transaction text will use more bytes in the public database.
The problem with these transactions is the following: it's customary to give some sort of "tip" (a fee) to the miner that adds your transaction to a block (puts it in the public database). If you don't give a tip, your transaction will be processed slower (or not at all). The fee is based on the size of the transaction, so the more inputs and outputs, the higher the tip will need to be.

The problem with these faucet dust inputs is that they're sometimes only slightly higher than the tip you'll need to pay a miner to put an outgoing transaction generated with the inputs you got from a faucet transaction in a block... So you might end up paying like 10% or more as a miners fee (tip) in order to get your transaction included.

If i missed something or made an error in this text, feel free to correct me, i'll edit this description to

Not completely normal, but i've had it happen before myself... as long as a simple restart fixes the problem, there shouldn't be anything to worry about
Actually, i'm running 2.6.4, so there should be an updated version available for you.

EDIT:
BTW: fair warning: if you keep on collecting dust ammounts from faucets, you'll need to realize it'll cost you a very high fee when you want to spend your coins.

If this is indeed the transaction you should be seeing in electrum, but you don't see it:

It should be viewable in electrum... Things you can check/try:
- open electrum, go to the "Addresses"-tab => double check if the address 18FYVBaaC5xYJscd8VuqJmMgLdHJqJajck is in the addresses list (please report back)
- restart electrum
- check the electrum version (help -> about; please report back)
- double-click the green dot in electrum, manually try out a couple different servers.

AFAIK, there might be a couple reasons:
1) it's the wrong address: the private key from 18FYVBaaC5xYJscd8VuqJmMgLdHJqJajck wasn't generated by the master key inside electrum (copy/paste error, virus, mixing up two of your wallets,...)
2) it's a gui-problem inside electrum (that's why i asked for a restart and to tell us the electrum version... in case ThomasV or Shorena see this thread, they might also be interested in your OS???)
3) the electrum server you're connected to might be lagging (altough, if i remember correctly, the green button at the right corner would turn yellow or orange or something... and there are 103 confirmations atm, so the server should be lagging by a lot to cause this)

EDIT:
BTW: since you're new at this: you did write down the electrum seed when creating a wallet, right??? You're asking for support, so you might need to "play" with the wallet, so you'll basically need to doublecheck your seed backup in order you mess something up!!!

Yes, there is...
https://blockchain.info/address/18FYVBaaC5xYJscd8VuqJmMgLdHJqJajck
This site is a block explorer, it should show all transactions that were included in a block (and even most unconfirmed transactions)

As you can see, the last transaction that should be viewable inside electrum should be this one:
https://blockchain.info/tx/95498a5e9b00be1da0e62e345b5bceb30daa737c7237fb072b76a8728a46601f
0.000697 BTC added to your wallet on 2016-05-09 17:36:16

Is this the transaction you're missing in your electrum GUI, or can you see this one?

No,
Electrum doesn't need to be running... Are you sure electrum is connected to a server when you were checking (is there a green dot in the right bottom corner?).
Can you post the address you were supposted to receive the coins on?

True, completely true, but i do think it's the community's task to educate new users about the advantages and disadvantages of different types of wallets.
I'd never recommend an online wallet, so i try to give all the pro's and con's about these kinds of online wallets (pro = easy accessible and small learning curve; con = you don't have your private keys with you, so you're basically not in controll of your coins). In the end it's still the user's choice.

Yes... Once you have 1 confirmation, you're pretty safe (not 100%, you can still be included in an orphaned block, but chances of experiencing this combined with a double spend are low)

If the block that included your tx is orphaned, chances are really high you were also included in the other block, or you'll probably be included pretty soon, unless you're a victim of a double spend

I hadn't looked to closely, but apparently, one of the inputs that were used to create the transaction that would have created the input for your transaction was also double-spend 2 days later:
https://live.blockcypher.com/btc/tx/a4c719d8df5f8cad33a7ea77bd30814633994c9ace9f48a8c53bdbd46f814fd3/

Pretty confusing stuff

It basically boils down to the following: if you want to know which inputs and outputs were created to/from your address, just open it up on blockchain.info (or any other block explorer). You should only panic if there are outgoing transactions that you know nothing about, because in this case you might have been the victim of a hacker, or at least somebody has access to your private key.

https://blockchain.info/address/12wvNzm2Q2g7ZbLP9weewZFN54ppJQ3QMr

Here you can see how much coins were added to your address (green), and how much coins were sent from your address (red). If there are transactions missing, it's usually because they were rejected or double spent. This also means that they weren't included in a block, so you can basically treat them as non-existant. It is possible that you were expecting incoming or outgoing transactions, but if they weren't included in a block, it's like they never happened (eventough you might have screenshots to prove otherwise ).

I'm not a native english speaker, so it was kinda hard to read your two posts... So instead of answering/replying to specific questions/statements in your first two posts, i decided to just analyse what happened

You're talking about two wallets:
12wvNzm2Q2g7ZbLP9weewZFN54ppJQ3QMr
1B3U9dWAc1A2ao6TxnkMmphL7sGoUGjQNu

You have problems understanding what could have happened with these 3 transactions:
5b241e4c4abe37424863f3075eb8e3bbcd19d7744b88bfa38c22c94513c1a240
fb195ed926d3c5aa364ebb76462faa3986415e14e8d53f4ca09c1159199cb649
950b4ff5842d078a8c20a59683c316790f7437546213766aca01fea59f925415

In order to do this, i'm going to make use of blockchain.info. All transactions that got included in a block are shown on this site. Rejected/cancelled transactions might have been removed, but this is not important because those transactions were not confirmed, they didn't make it in any block, so you could still use their inputs to create outputs (unless the inputs were used to create a double-spend). The screenshots you show might have been things you actually saw, but they don't really matter. The only thing that matters is which transactions were included in a block (confirmed)

I'm also going to use live.blockcypher.com because it sometimes keeps rejected transactions in its database for a longer time.

Transaction 1 :
https://live.blockcypher.com/btc/tx/5b241e4c4abe37424863f3075eb8e3bbcd19d7744b88bfa38c22c94513c1a240/
2 inputs, 2 outputs, confirmed

Transaction 2 :
https://live.blockcypher.com/btc/tx/fb195ed926d3c5aa364ebb76462faa3986415e14e8d53f4ca09c1159199cb649
was received 12 days ago, but NOT included in any block, because you got a double-spent message, the transaction was probably still unconfirmed, but rejected by blockchain.info's node. This means they allowed you to create a new transaction 2 days later, using the same inputs as the one used for this transaction. So they allowed you o create a double-spend, which was shown on sites like blockcypher, but maybe not on blockchain.info (because they rejected it).
This transaction had 6 inputs,
input 1 was spent 10 days ago: https://live.blockcypher.com/btc/tx/950b4ff5842d078a8c20a59683c316790f7437546213766aca01fea59f925415/#spentby-f98f907fbeab39791debe43d2d372124298266ce064fe631d59b8faa1b556772-0
input 2 was spent 10 days ago: https://live.blockcypher.com/btc/tx/950b4ff5842d078a8c20a59683c316790f7437546213766aca01fea59f925415/#spentby-c75649c3a4038af0181a02e89bc68691669b426d53ab87ab1aea03234e7a8aef-1
input 3 was spent 10 days ago: https://live.blockcypher.com/btc/tx/950b4ff5842d078a8c20a59683c316790f7437546213766aca01fea59f925415/#spentby-3f46635d9a6793dad438eb9a5d73f6a25b8e07b78b82133b2d18a958b70ea714-1
input 4 was spent 10 days ago: https://live.blockcypher.com/btc/tx/950b4ff5842d078a8c20a59683c316790f7437546213766aca01fea59f925415/#spentby-cc46866f39f81c7fd5d860d5188f66505f0373b30f0ea97ae6289ec0bf8371ee-1
input 5 was spent 10 days ago: https://live.blockcypher.com/btc/tx/950b4ff5842d078a8c20a59683c316790f7437546213766aca01fea59f925415/#spentby-5b241e4c4abe37424863f3075eb8e3bbcd19d7744b88bfa38c22c94513c1a240-1
input 6 is unspent: https://live.blockcypher.com/btc/tx/d76f0516e54c87c54f9563cf2003ac638b43e51b279de6e668d9ecac9ddd5999/#output-index-1

Transaction 3 : https://live.blockcypher.com/btc/tx/950b4ff5842d078a8c20a59683c316790f7437546213766aca01fea59f925415/
This is the confirmed transaction in which you double spent inputs 1-5 from your transaction that was rejected by blockchain.info

Indeed, and in the OP he said 12wvNzm2Q2g7ZbLP9weewZFN54ppJQ3QMr  was his blockchain.info wallet, thus he created the double spend himself after blockchain.info rejected the first transaction on their node

https://blockchain.info/address/12wvNzm2Q2g7ZbLP9weewZFN54ppJQ3QMr

On april 21, there wasn't any confirmed transaction of 6.8 BTC, and after this date, no transaction of 6.8 BTC has been made...
since transaction 950b4ff5842d078a8c20a59683c316790f7437546213766aca01fea59f925415 is also using inputs from your own wallet, you probably double-spent your own inputs and got the first transaction cancelled

EDIT:
In short, you had inputs, created transaction https://live.blockcypher.com/btc/tx/fb195ed926d3c5aa364ebb76462faa3986415e14e8d53f4ca09c1159199cb649/ which was rejected by blockchain.info.
Since you used blockchain.info as a wallet, the inputs from the rejected transaction could be used again, which you did for transaction https://live.blockcypher.com/btc/tx/950b4ff5842d078a8c20a59683c316790f7437546213766aca01fea59f925415/.
This second transaction got confirmed, thus cancelled the first transaction

To answer your questions:
1) you need inputs and outputs... If you don't have inputs for a 6.8BTC tx, you cannot create valid outputs either
2) same answer as 1)
3) they don't have an unencrypted version of your private key, they would need your password to access your account
4) no, you just created 2 transactions with the same inputs