Where does the money come from when mining?
They are generated when a specific mathematical equation is solved by the mining software. Since it can't cheat (=must use brute force approach) and since the system is well designed (=mining difficulty) not "BTC mining flood" can occur.
Who pays for these useless calculations?
You! And they aren't useless since they generate bitcoins for you.
I mean at the end you simply get money from a other person when mining right?
No. You get it from the system itself.
Or is this simply money for free? (if we don't look at the electricity bills ofcourse)
No, because it costs
at least the electricity.