Mastercard uses EUR as a clearing currency and VISA uses USD, but the technology is more or less the same. Also, the debit and credit cards are not the money itself, they just link together the payment's initiator with the payment's recevier and they handle the communication between them.
The cards act like the mobile phone when you start a bitcoin transaction from a mobile wallet. They are the technical part of the system.
According to OP's example, it's like merchants will accept bitcoin, but they will use stickers on the shop's door to show what kind of mobile wallets (or bitcoin payment processors) they're accepting when it's about paying with bitcoin.

Thanks for the clarification. So as long as I don't combine the addresses (I have received the coins to) with each other when I'm sending a transaction, it seems that they're totally different and they haven't got any connection. If I have e.g. 10 addresses in the wallet and I receive 0.001 BTC for each address, nobody will be able to tell that in my wallet I have 0.01 BTC because they can't tell that the addresses are in the same wallet.

Use some kind of physical wallet (paper wallet, as mentioned above, or hardware wallet).
Create backup, don't create only one paper wallet, but some, and put it into trusted a safe locations.
Or, if you want to move your bitcoins (or part of them) sometime in the future easily, you can buy a hardware wallet (Trezor, Ledger Nano S), make sure the device has an own screen to verify the addresses and to be able to securely write down the seed (12-24 words, a kind of backup for your hardware wallet). What you really need is the seed, not the device itself, because if the hardware wallet e.g. crashes, you can buy another one and set up with your seed, you will see all your coins on the new device again.
Place your seed in a really safe place, in local and remote locations. If you haven't got someone you trust 100%, you can divide your seed into two parts and give half of them to 2 people (preferably, they should not know each other),  to store it safely, because they can do nothing with the half of your seed.
Don't worry, but think about the possible risks and take the necessary steps to handle them.

I know that a hardware wallet (Trezor, Nano S, etc.) generates a seed and after it gives you nearly unlimited number of addresses which you can use to transact using the same wallet. It's adviced to use an address only once, to minimize the possibility of linking addresses and historical transactions together.
My question is:
Is it possible to link two addresses, generated from the same seed, based only on the common seed? (if there's no transaction that can link the two addresses together, even in the history of addresses?)
Is there any mathematical procedure to verify that two addresses are generated from the same seed?

If the fee is below 10 sat/B, the viaBTC accelerator can't help, because despite of they're free but they need to have a little profit on every accelerated transaction too. Usually the small fees are higher than that even in case of a low cost transaction is choosen in the wallet. Without tx number, we can't even check the sat/B of the transaction, because it not only depend on the fee itself but the size of the transaction (inputs, outputs, etc...)

If he already owns a few bitcoins, there can't be a real need to invest more and more, and risk the house and everything he has gathered. But, if he has a few houses, it can be a wise decision. Anyway, if he want to risk it, and he can afford to risk it, then risk it. He has 50% chance to win and to lose... In my opinion the way forward for the price is still up, but there could be some bumps on the road now, there won't be an easy ride... There are too many people investing now and fees are high, mempool is full. If LN starts that could help a lot, until then, we need to be careful...

Existing fiat currencies are going to be digital in some years time. As smart mobile phones are spreading all over the world, the forms of payment will change and we'll use less paper and coin as money but debit and credit cards as well as debit and credit cards digitized into the mobile phones (using NFC payment method like MasterCard's PayPass solution). It's not bitcoin which will replace the physical money but the digitalization (that contains bitcoin, too). But, digitalization will help bitcoin, at the end, because if people will get used to pay with their smartphones, they will accept easier the usage of bitcoin on the same smartphone. Bitcoin will be just a 'foreign' currency for them, just like if you live in the EU, you know USD and maybe you have some USD as well, but it will always be a 'foreign' currency for you, but this won't stop you trying and using it, as well as trying and using bitcoin in the future.

I hope that the coming holiday season will give bitcoin some time to recover. I hope that people will spend their fiat on buying presents and not too much bitcoin for a while now, and for the beginning of 2018 the lightning network will start to operate (or as soon as possible). Poor developer guys at LN, they are under heavy pressure now, I think... (and of course, every other developers in the bitcoin ecosystem too...)
My fear is that this is the time when the average people try to invest in bitcoin and bitcoin have to show that it's competent and fine not to scare away the people with sky high fees and slow transactions... We need to survive this period, somehow

There's no need to worry, the bitcoin network is running full speed for some time now, mempool is always full, this is not news anymore. To have a confirmation in one hour you need to include decent fee in the transaction, to get the miner's attention (they're hunting for transactions with high fees).
You haven't included any detail about your transaction but if you use an accelerator (and have a little luck) you can have your transaction done really quickly, as you have already experienced it.
Spreading FUD is not necessary...

It's the time now for the Average Joes to hear about bitcoin because bitcoin is in the media already and now a lot of people are aware of the potential of bitcoin. Some of them want to try it and invest a little amount ($10-$100 or so). They don't know about the technical background, they just heared at the hairdresser that somebody has multiplied his investment by 10 last year with bitcoin, so why not to give it a try?  If bitcoin crashes now, they won't be back again in two years time and that would be really bad for bitcoin. Just imagine: 'Yes, I've heard about bitcoin, I've tried it, I've put my $100 in it and it has crashed, I lost nearly the whole sum in some months...' This is what we don't really need now, to scare away the average people

What about sending it in a password protected zip file with a really strong password? Using a really common file name like IMG_0001.zip?  If sysadmin has luck and can spot that the zip file doesn't cointain a real picture but a wallet.dat, he won't be able to brute force the password soon. Just an idea

Bitcoin is not for small everyday purchases as of now... You can make small transactions but you should be lucky with the fees or use an accelerator or to pay really high fees. It only worths the time/cost/effort if you are in a real need. Else, you can just hold your bitcoins and use your fiat instead, if you can, and expect bitcoin to grow more. I have bought a few years ago a coke with bitcoin. I don't want to calculate now, what is the price of that coke, if I calculate it with the exchange rate today...

Big bitcoin holders are smart enough if they want to sell their coins they won't pour them on the market at once... If they do, the price will crash, but if they just sell them piece after piece in small portions, it won't drop the price. It takes more time to sell the bigger portion, but it worths the time and the effort, because they will get proper earnings on those transactions. Also, I think this kind of sell can be automated thru the api of the exchange, so they don't need to sit next to the PC the whole day or so, because trading scripts can do this for them.

Trezor or Ledger Nano S is equal in functionality but only the price that makes difference.
Online wallets (not giving out private keys) are not safe, so you should only store little amount of bitcoin in online wallets. Other wallets on the web are a bit safer, if they give you your private key or seed, but you should consider that if you have to use your private key or seed on a webpage to interact with your wallet, you have to input it on the webpage. There are several possible points of attack: Keylogger built into keyboard, keylogger built into the OS on the PC, malware on the PC, phising website to grab your key, or man in the middle attack while your key are on the way to the website (travelling on the web from your PC to the wallet's server).
If you use a hardware wallet, the private key or seed won't be shared with anyone (PC, keyboard, internet, website, etc.) With a hardware wallet, you only send signed transactions from your PC, from which the private key or seed is not extractable. Everything in the process that needs a private key happens on the hardware wallet itself this is why they are really safe choice.
You pay for this safety and not only for a wallet itself.

You can't compare the two digital money. Bitcoin is decentralized and a way new technology. Digital USD already exists nowdays, but now we call it debit card and credit card. The new digital currency will be only the substitution of the phisycal card to e.g. a mobile wallet app for that digital USD currency. (It means, you won't need a card to access your funds in the bank if you want to withdraw money or pay at a POS terminal. You will be able to use your smartphone to pay or to withdraw). The technology behind is not so interesting for the average joes. They don't care if their payment goes thru a centralized system (VISA, MasterCard, AMEX payment processors' systems) or just uses a blockchain technology. Bitcoin system is totally different, it's not just digitizing the current system, but it's changing the whole process from the beginning to the end.

Bitcoin is now on the way to get known by more and more people. This means a higher demand, which can help to sustain the price of bitcoin for a while. This could be enough to finish the development of the LN and the Atomic Swap. If they go live, that could solve some major problems of bitcoin, like fees, transaction times etc... which also can help the price not to crash.
Also, if governments start to regulate bitcoin in order to get tax out of it, can make some negative effect on the price on the short run, but on the long term it could help bitcoin to be an accepted digital payment method.

There's a good article about Lightning Network on coindesk:
https://www.coindesk.com/lightning-bitcoin-scaling-tech-really-know/
They say that LN has a great potential but the deadlines are a bit far away yet, so we need to wait some more time to start using the Lightning Network. On reddit they talk about the similarities of the Lightning network and IOTA. This LN topic is in the news now, they have already named it blockaccino...

There's no really need to understand bitcoin for the average joes. Like they don't really understand the technology behind e.g. smartphones, but they can use it pretty well. They know a lot about their outfit, does it have an apple logo at the back or not and they can easily judge them without any technological knowledge.
Maybe this will be similar to bitcoin, the average joes will only need a good application on their smartphones to use bitcoin and they won't care about the background at all. They will also judge the different alts as well, based on news from unreliable sources, but that's life.
I won't mind if people don't understand bitcoin as long as they are happy to use it...

It's nothing about trust in connection with the exchanges. No one really trust the exchanges, but everybody have to use them if there's a need to exchange cryptos to fiat or cryptos to cryptos. The real question is how to minimize the risk for the period of time when the funds/coins are on the exchanges. This is where you can search for well-known and widely used exchanges. Those exchanges will have the less possibility to scam you which has some regulation already in their country.
There's another kind of exchange where you can minimize the risk, those are the decentralized exchanges (like etherdelta) where you can directly exhange cryptos without any need to trust anybody/anything. Unfortunately this only works for ethereum tokens yet, and in my opinion this is hardly possible to implement in connection with fiat.

Well, bitcoin is wasting some electricity, that's OK. What I don't think is that Bitcoin uses as much electricity as banks. There are a few really big banks where only the HQs and the branches in capital citys use as much energy as Bitcoin itself with miners and users, etc. Big banks has not only HQs but branches at the countryside too, ATMs, etc, so they use way much more electricity compared to Bitcoin.
From this point of view, bitcoin can save some electricity compared to banks and can do the international money transfer with much less consumed electricity than a bank.