3.
https://blockchain.info/address/19SxkCSLKKpyqrQZ4BAFbQVCGiVBVPDYWLThat address is mine, apparently, but it is not specified in the Bitcoin-QT client. But somehow it seems that whenever I send a transaction, the official client sends the remainder of input(s) to a new address (which I do not have in the list) and somehow does not lose track of it's public and private key. How/Why does this work/happen?
These are "change" from any transactions you've sent in the past:
With the way bitcoin works, you can't partially spend a previous output that you received. It has to be completely spent. So, if you receive 10 BTC all in a single transaction from someone/somewhere at an address, then that address now has a single 10 BTC output.
Later if you want to send 2 BTC to somebody, the program can use the previous 10 BTC output as an input into the transaction, and create a 2 BTC output to the address where you want to send it. This leaves 8 BTC leftover in the transaction. If you don't send those 8 BTC somewhere, then they become miner fees and end up in the coinbase transaction of the new block for the miner to keep. If you don't want to give those 8 BTC away as fees to the miner, then you need to include a second output in your transaction sending the 8 BTC back to your own wallet. As an analogy, think of pulling a $10 bill out of your pocket to pay for something that costs $2, you get $8 back in "change".
The way Bitcoin-Qt does this is to create a new bitcoin address that it doesn't tell you about and keeps track of that address and the associated private key in your wallet.dat. Since this isn't an address that you requested in the "Receive Coins" tab of the user interface, it doesn't show up in that list. Bitcoin-Qt knows about the address since it is in the wallet.dat file, so it includes it in the balance that it shows you. Bitcoin-Qt uses a new change address for every transaction. So if you create 10 different transactions, each sending bitcoins somewhere, then your wallet will have used 10 different change addresses (although some of them may be empty if Bitcoin-Qt used the bitcoins associated with some of those address as inputs into other transactions).
You can get a list of unspent outputs that the wallet is tracking by using "listunspent". It should give you the transactionID, the vout, and the BTC value of each unspent output in the wallet. This should be everything you need to create your raw transactions, but if you want to choose particular "sending addresses", you'll need to look up each of the transactionID and vout to find out what address the bitcoins from the output are currently associated with.
* I've been working on a Perl script that makes a listunspent API call to Bitcoin-Qt and then parses the output presenting a list of all the useful information about each output. It needs a lot of cleaning up and beautifying, but I think I got it working a couple days ago. This is step one of my attempt to create a perl program that will automate sweeping dust balances together in the wallet, as well as automating other processes (such as sweeping balances out of old addresses into a paper wallet).
