So if iam understanding right this mining is only to generate new coins so they will that will get into your wallet (the bitcoin economy) at a X rate?
No, CURRENTLY mining serves two purposes:
1) Expand the economy by mining bitcoins and putting them into the market (currently 50/block solved)
2) Confirm Transactions
In the future, when all of the Bitcoins have been mined (around 2030 and 21,000,000 coins), mining will not generate new coins. At that point mining will only be for confirming transactions (by adding them to the block chain).
Why will miners mine? Because of the transaction fees, because the miner who adds a block to the block chain gets to keep all of the transaction fees for that transactions that were in that block.
If miners didn't exist, neither would Bitcoin.
So at the end you are creating money since you started with a X low amount of USD/EUROS paid for the electricity wich you can turn into Bitcoins by mining them and wich also are more worth in USD/EURO or any other daily life currency then you started with/put in. And 1 BTC is not realy earned by doing some usefull computing calculations wich would be the explanation that you earn money by mining, right?
So where does the money come from that pays you for mining or even better said, pays you for the profit you create for your self? This cannot be the system since then as explained above you would be creating money out of thin air.
And creating money is not legaly possible, right? So at the end the only explanation for that you get money for mining is that somebody pays you the differential in real USD/EURO for mining/calculating nothing (sorry) ?
Miners don't create money, they "find" it. Just like miners of gold don't make gold. Resources are expended to mine for Bitcoins (electricity, hardware to mine (which wears out and has to be replaced), and time) just like they are expended for mining for minerals.
So to rephrase my question. Where does the USD/EURO come from that pays your profit you get when mining?
Miners are able to do whatever they want with the Bitcoins they receive and/or are paid.
Your question is one of economics and is a question for everyone who owns Bitcoins. How do you realize the value of a Bitcoin?
The same way you realize the value of a Dollar/Euro. You spend it on something else that has value to you.
So, miners can buy products, services, and entertainment with them. Or on exchanges, they can buy other currencies (like Dollars and Euros). Some just hold them, hoping they'll be more valuable in the future than they are today.