For example I would like to filter a list of elements (Module built with MOST) against the current user, so that he can only see his own.
Would that be possible with the options given in the Blocks administration?
I don't think so. Blocks are filterable based on the current information in the query parameters and the request attributes. This includes stuff like `_locale` and `_route` as well as anything you might add to your own query like `pagenum` or whatever.
In order to filter by uid, you would need to add that to the query params or attributes somehow. But this is not standard in most queries.