@LvM: Like others have said before in this thread, you fail to see what Bitcoin really is, because you keep thinking in your own environment of bank accounts.
What Bitcoin tries to resolve is something completely different !

Let me try to explain the basics:

Centralized versus decentralized:

If a person A has a bank account with bank B and wants to send some money to person C that has a account at bank D, then this is what happens in your world LvM:
person A gives bank B (and only bank B) the authority to "send" the money to bank D. This involves central authorities (bank B and D) that have to be trusted: bank D trusts bank B (that the transaction is legit, that they are not double spending money or creating money out of thin air), and person C trusts bank D that he can get cash from his account that was credited.

I suppose you can understand the above (and probably better then I do).

Now LvM, ask you the following question: what happens if there are in the above scenario NO BANKS involved AND A and C don't trust each other (as they are strangers) ?
To put it in other words: person A wants to send some money to person C. (And afterwards, person C should be able to spend this money to another person E)

This is exactly the problem that bitcoin solves !

We have two problems:
 1. C will only accept the money if A can prove he "owns" the coins: that is why the transaction is signed cryptographically by A to prove he owned the coins. And with the transaction, all coins are transferred to an address "owned" by C (that is, only C can sign the spending, as he is the only one that knows how to), and "the change" to another (or the same) address "owned" by A.
Due to the crypto-magic, C does not have to trust A: he can easily verify (and everyone else looking at the transaction) that the signature is correct, and the signature is nearly impossible to compute by anyone else then A.

 2. A malicious user A could try to send his coins not only to person C, but at the same time send them to X (here is your impossible double-spending). Both C and X can verify the signature, which will be correct. But which of those transactions is the right one ? The solution that bitcoin offers here is the "proof-of-work" blockchain: the transaction that is recorded in the "best" blockchain will be recognized by everyone as the correct one. Nobody needs to trust anyone, no bank needs to authorize something. NICE, ISN'T IT ! The company you work for is not necessary anymore

So here you have it:
I want to spend Y coins I received (from mining or from others) to person Z: I make a transaction and send it to the network. After a while, it will be included in a block, and after some more time, it will be "buried" deep enough in a chain of blocks so that it becomes nearly impossible to change it: now everyone in the network will happily accept that person Z owns Y coins.

I know that. Saw it cited or as link in wikipedia, bitcoin.org or so, perhaps on Bruce Schneiers own website.
Could and can do nothing with that. You? Why?

As said, encryption is quite a different problem anyway. 
Bad idea to mix money transfers or (likewise) the content of emails or anything else with their encryption.
I am interested in the basics, encryption is another level.
Didn't even try to talk about encryption at all.

Thank you!
So the block time is comparable with a bank working day, even the time.
Yes, fine! Have no problem with that!

Remains the problem of the "changings", but that seems to be a (self produced but anyhow solved) pure technical problem only.

That there is no field "reason of payment" remains as really significant disadvantage.

More fundamental, the 21 Mio. limit which almost alone makes BTC interesting for me is in my eyes not really guaranteed.

The so called "community" might change that some day, accepting a BIP concerning this matter if they like and are so silly. Technically it seems easy, enough to change just one public variable. But I am not sure, of course.

Sure, but the discussion is sort of entertaining at least.  If he's a troll, he's one of the more entertaining trolls I've communicated with.