Is it okay to ask your professor about the final exam that I took 3 years ago?
It is completely fine for students to request to see their final exam scripts. As a lecturer, I am actually surprised and slightly frustrated that many students seem to be only interested in their mark, not the feedback.
However, asking for an exam dating back 3 years may be a bit more difficult. Exam papers are only kept for a particular amount of time, often ~3 years. So if you want to ask, do it as soon as possible before your exam paper is discarded.