Yes to all of your questions. I personally like to bring cash and then if I run out I have my credit card. Some credit card companies will charge you a certain percentage to do the conversion. I'm fortunate in the sense that mine does not. There are ATMs on the island that will give you Belize money not American. And most places will take Travelers Cheques.
Lola, definitely check on whether your credit card company charges a fee for using it there. It can be a nasty surprise when you get the bill. I've had no trouble getting traveler's checks cashed there. I'm leaving for SP tomorrow too--maybe I'll see you there!