admin/content customizing I need to add some new filters to the admin/content (or admin/content/file) page. Standardly, it offers me just type and status. Let's say, I would like to add the filter "name", that shows just the files of specified author. I am able to generate all the possible authors (their names) from SQL table, as well as showing them on the page (simple add it to $form['filter']['filters']['status']['filters'] with hook_form_alter function).

But now I do not know, what to do next. The submit button calls some function to generate some filters (but then it seems pretty difficult to change everything).

Do you know any way to do that?
Try Administration Views module. It comes with views based listing. Which can be easily modified based on our requirements.