After some time of reading about the topic I still dont understand some things fully. So i have some question.
A block is a record of some Transactions plus data that links it into the global block chain.
* Is the global block the same thing that is called merkl root?
The Merkle Root is a hash that represents all the transactions grouped into a tree structure in such a way that transactions could theoretically be checked without needing to download all of the transactions. See http://en.wikipedia.org/wiki/Merkle_tree
Mining means working on a block and finding a hash that has a value below a certain difficulty.
* Is "finding a block" a synonyme for finding a hash that is lower than the difficulty? Or is the block the one thing and the hash for this block the other?
* Is mining of some worth because the found blocks are easier to store or is it another thing?
1. Almost, except the hash has to be lower than the target, not the difficulty. The target is the maximum target divided by the difficulty.
2. Mining is of worth because it confirms that you have done work for your 50 BTC subsidy.
Then the block to work on is always special because your bitcoin-id is part of the algorhythm you work on. Which means everyone has another problem to solve. Because of that it doesnt matter how fast you get your block through jsonrpc or directly from the network.
* Or do you have to care about this speed?
* What happens when there are more than one correct hash that solves the same block?
You have to care about this speed because each block has to contain new transactions. The only block that you get paid for is the one that the majority of the network accepts. If somebody solves a block and then you make another version for the same point in the chain, the other nodes in the network will reject yours. This leads to what are called "orphaned" blocks. So you want a good network so you are informed promptly of a solution being put out there so that you can start on the next block in the chain instead of wasting your effort.
Finding a block is randomly happening. You send the result into the network to verify and...
* When will you get a reward? Is this randomly given away for one random correctly solved block?
* Its not the case that exactly every 10 minutes these blocks are given out isnt it? Otherwise i think it could be exploited...
You get the reward when your block reaches maturity. Currently that's fixed at 100 blocks in the client. (About 1000 minutes, or 16 hours.) You are correct that the blocks are not solved exactly every 10 minutes. It's a random process. The algorithm adjusts the difficulty based on the past network performance to try to obtain a 10 minute average time to solve every 2016 blocks (about 2 weeks).