Now my problems: How can I keep my screenshots and movie posters?
Screenshots—I don't think so. If posters are saved outside the database, they can be imported or re-associated with movies in a new database using the procedure described
here.
But rebuilding a database is a lot of work. The problem you describe does not necessarily suggest database corruption. If I were you, I would want to verify what the problem is before heading down that road.
Without any notable logic the number of films that have to be imported rises.
This seems to be the thing to focus on. If this is happening with any plugin and with any new movie name known to be unique at the source (i.e., the problem has nothing to do with the plugin finding the right movie at the source), then that might suggest the problem must have something to do with the database. When a plugin finds multiple movies, are you selecting the one you want downloaded, or instructing it to download them all?