I see that I have 1 free domain registration included with my hosting plan, but when I try to register it still wants to charge me. Is that because I'm on my 2-week trial?
Correct. DH has to fork out some money to get the name registered. But you will be entitled to a free registration after you pay for hosting.
You can use a free dreamhosters.com subdomain to test out your site. The free domain registration is a $9.95 credit on your account.