How can one see all pictures which are processed with a specific filter preset? Is there a way to do this? I need to change a preset for all pictures processed with it.
By Filter Preset I assume you mean a Develop Preset. The metadata filters for searching can find a preset if (and only if) it was the last thing done. If you modify the image further in develop mode, the information is not searchable in Lightroom, so the answer is "except for special cases you cannot" in vanilla lightroom.
That said, the information does continue to exist in the develop history, so for any given shot you can scroll back through the history and see if the preset was used. That is clearly not very helpful for finding shots affected by it, though it can confirm it.
The only way I know to find if a shot was once affected by a preset (and then overwritten by other changes) is to use SQL and look through the Adobe_libraryImageDevelopHistoryStep, or write a plugin that does so (I am not certain if this is visible to plugins).
Direct access to the catalog via SQL is possible but not supported by Adobe and the file formats are not documented; that said they are in plain text (mostly) and reasonably searchable. This is a quick and dirty SQL statement that I think will get your close to what you want, substitute the full preset name in quotes:
select rf.absolutePath, f.pathFromRoot, lf.idx_filename from Adobe_libraryImageDevelopHistoryStep ds inner join Adobe_images i on i.id_local = ds.image inner join AgLibraryFile lf on lf.id_local = i.rootFile inner join AgLibraryFolder f on f.id_local = lf.folder inner join AgLibraryRootFolder rf on rf.id_local = rootFolder where ds.name = 'Preset: General - Zeroed'
The SQLite Manager addon to Firefox is a good way to access the catalog via SQL, though there are many tools. I strongly suggest making a copy of the catalog file (the .lrcat) and using that when experimenting, instead of the real catalog.
This will not work if you deleted the develop history of course.