Is it normal to have a thirteen year age gap in a relationship?

That's called ephebophilia.

Nah, that's fine if you two love each other. I've seen bigger age differences in my family

I would really like to say yes, but having been in (and observing many other) relationships like that, I can't endorse it.

If you really feel like he's the one for you, go for it.
But remember you're still developing. We all are, until around 25ish.

If you have doubts, don't be afraid to confront him about them.

No. You're still figuring out college and shit, he's a full grown adult.