I personally don't have any fan characters (FCs). I only have OCs. However, not all my OCs can fit in every RP, so yes, I do change my characters as needed to fit a RP. So, you could do the same with your FCs. Like if you have a Pokemon trainer, you could take away his Pokemon and put him in a modern day setting. Ask yourself, "What would he be like in a different universe?" 

As for animals, I rarely see role plays about animals, but they do exist. So you could probably find / make something for animal RP. Although rare, when I [i]do[/i] see animal RP it's usually wolves or horses. Sometimes lions.