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Hi,
I have now finaly an algorithm which makes it to level 513, but sometimes my algorithm didn't find any solution for the puzzle. I could avoid this problem by requesting a new puzzle and searched for the problem with my solution, but I wasn't able to see the problem. So my question is now: Are the puzzles always solveable?

All the puzzles I experienced were solvable. That's not to say that "all the puzzles are solvable", but given that the puzzles will probably have been made 'in reverse' - taking a grid, deciding on an answer that the puzzle will have, then making sure that the path is free for that answer, before adding 'distraction' paths - I'd say it's pretty likely that all of them are solvable.
You could PM me a text version of one of the 'unsolvable' puzzles?