Most likely, they do bathe because after alot of battling you would get sweaty. And no characters said "Phew, you stink!" so I assume that they have bathed (Or they have REALLY good deodourant).

But I know for sure that characters eat because in FF IX Zidane meets Freya in a pub (He was getting soup du silence) and the characters eat after the fesstival of hunt. I can name many occasions in most FF.