Some further questions:
Couldn't someone just creates a whole lot of addresses and then submit with every address the needed amount, so he can win the lottery safely?
Ticket distribution is controlled by purchasing them with the number of coins equal to the stake difficulty, so increasing the number of addresses for coin concentration is actually deleterious (there is an input quantity limit).
I can't see any incentitive for runnig full nodes, which is a problem as you might see at bitcoin. How about the idea only full nodes receive tx_fees(running a wallet with full blockchain) and miners not?
Full node running is incentivized by the PoS system, who have it in their personal interest to ensure that abuses of the blockchain (weird tx types, tx exclusion as seen with bitcoin) does not occur.
Where is the incentitive to submit tickets? When there are no "fresh issues", you will probably earn as much, as you submit, but ypu can't use a part of your coins. This will end in nobody submitting tickets.
If you don't use your ticket to validate your block, it becomes invalid. So you are strongly incentivized to vote on your block, unless you'd prefer to lose your reward.
Or maybe, i didn't undertsand it correctly and everybody gets their money afterwards back and the lottery winner gets a reward for the block he submitted. Which one is right?
As far as I understand, even people, who didn't win in the lottery, can use their tickets, to sign a block. Otherwise it would be really insecure
Only persons with tickets corresponding to the lottery winner number can sign the block.