For some reason, when I go to battle, it won't let me challenge an opponent because it says that my pets are unhappy and hungry? :/ But I just fed and um. Happy-d them until the bars were completely full. Am I doing something wrong? Is there some other kind of reason why it won't let me battle?

Quite possibly your pet is stuck in a battle. Go to the stats page at the top of the Coliseum to check. If not, check out my Battle Guide in my siggie. It gives you step by step instructions on how to figure out why you're stuck.