Hi Thomas,
godaddy is, to my knowledge and experiance, a good company (i have a domain from them that i have never had problems with).
1)Is the hosting up? did you get an e-mail with a password or something? you should be able to access the hosting even without a domain...
it would probably look like:
http://hosting.godaddy.com/~user_name
but i wouldn't really know because I never got hosted there.
if you did not get any e-mail from them:
-check that your e-mail address in your godaddy profile is correct.
-check that the transaction was actualy completed (ask your mentor to check his bank statement or something..)
-email godaddy.com explaining the problem.
2)regarding the domain... it can sometimes take a long time, even more than three days for the domain to propagate throughout the nameservers... try from a computer that has a different ISP, and also just be patient for about 48 more hours...
hope that helps!
-Leav