[El Diablo]

Well, i don't think Mihawk has eaten a devil's fruit. Don't you think it would take away from the fact that he's the strongest swordsman in the world? As for cutting the ships (manga spoiler)

Spoiler:

Zoro develops a technique that allows him to cut things without actually hitting them with his sword. I'm assuming Mihawk is doing the same thing essentially to cut the ships.