Member ControlPanel Logs? Are there some logs which tell, what the member does in the backend?

Something like: "User: «John Doe» Edited this entry at this and that date".

Just a bit more information than what is written on the member account:
Not currently... we've discussed adding a sort of audit or activity trail to Craft itself, but haven't flushed out any details or timeline.

In the meantime, you could probably get 95% there with a custom plugin that listens to the various Craft events you're interested in.