As others said a plugin is probably the way to do this. Depending on when you want to redirect users an event plugin might work. For example, you could target the "u_login" event so when they log in they go to the correct category.
Check against qa_get_logged_in_userid() to redirect specific users, then called qa_redirect() with the appropriate path. You might want to make yourself an admin form where you can enter user IDs and the categories they belong to, and store that in an option.
For filtered questions Onurb is correct, you'll need a page plugin that fetches posts according to your own criteria, then displays them on the page.