Is it normal for a 35-year-old male to fancies a 22 year old female (me)? I don't feel comfortable dating/fancy a guy who is a lot older.?

Then don't date him. The chances are his fancy is mostly superficial anyway. 

A few years age difference shouldn't be a problem, but a 13 year age difference is, in my opinion, too large a gap.  Also, you say that you're uncomfortable--which is enough right there.  Don't get involved.

That is up to you. If you don't feel comfortable then don't. It is not wrong though everyone has their own standards 

Yes its normal, you're young and beautiful so no surprise. Everyone has a preference and in your case you dont do older men, so if he hits you up tell 'em you're not interested.