Fertilized eggs, how to tell?

Hi everyone, I am new here, and new to having chickens too!

My daughters class was hatching some eggs last spring, so we decided to take two chicks home to raise.

They are now 4 and a half months old, one is a hen and one is a rooster, and the female just started laying eggs, very exciting stuff! I haven't seperated them, they live in their coop that hubby built together.

How can I tell if they are mating, and how can I tell if I have fertilized eggs or not? Should I seperate them?

I wouldn't mind having a few more, but mostly I just wanted a few to raise for fun and for eggs to eat. I don't want or have room for lots of chickens.

Any advise would be appreciated! Thanks!!