If I buy a domain name, is there a way I can transfer the pages from my free hosting account to that domain name? Do I have to buy a hosting package or can I just add a domain name to my existing account?

A domain name doesn't provide hosting - you will need to direct your domain name to whereever you have the site hosted.

That's what I'm trying to figure out... I have a free site with Bravenet, so can I just use the domain name for the site I've already built?