DannyHamilton thanks a lot! It is all clear now.

So it is possible to set the fee to my needs(For example 0.01 per transaction).

I only need to make something so the user who does the transaction doesn't see the transaction that comes back.

That makes it a bit clearer. But I still don't fully understand the raw transactions.

Here is an example of how I now think it works. Can someone correct me if a step is wrong?

I have an unspent transaction with 1 bitcoin.
I want to move 0.5 to another address.
But because the unspent transaction is 1 bitcoin, the whole bitcoin will be send.
So I send the rest back to my own address.
So there is going 0.5 to the other user. And 0.5 back to me.
Does this mean I don't pay any fee? Or do I pay fee but the user doesn't receive the full 0.5 bitcoins.
And if I for example sent 0.49 instead of 0.5 back to me. Do I now pay 0.01 fee?
And do other wallet also work with sending the rest back? I can't remember that I can any incomming transaction after I made a transaction.

When I send a raw transaction, all bitcoins from the unspent transactions that I have selected will be send.
But how can I set the fee?
Do I have to send what I have paid to much back to my own address?

And I see a lot of people talking about that I can't know the fee before creating the transaction. But when I use 3 unspent transactions, and sum the amounts. I know exacly how much I send right?