Depends on the species, some pest crabs get pretty big. I can't give you a definite ID. He could likely get palm-sized if you give him food now and then.
The peppermints are probably safe, he's a bit slow to eat them and they sleep in holes where he can't reach when he grows. He won't go after the snails, most likely, since they live in the sand. Just feed him bits of shrimp or fish now and then to keep him happy.