They are mainly piscivores in the wild. I've kept 3 in the past and never had a problem getting them to eat frozen silversides, tilapia, prawn, krill, etc. I also used to feed live crays and small cichlids, although it took a while for the cichlids to get eaten. They are nocturnal lurkers and only need to be fed 2-3 times per week.
Yes, shrimp would be a fine start. I would try to include whole fish (guts and skeleton included; not just filets) as part of the regular diet.
These will not eat snails in my experience. The puffers that feed mainly on fish in the wild don't get overgrown teeth like the other species. I don't feed whole Tilapia, but I use frozen Silversides or home-bred live ciclids. Whole Tilapia at the stores would probably be a pretty big fish. You can buy frozen packs of Silversides at most LFS; they are slim and only about 3" long. You can feed earthworms, but blackworms/blood worms will probably be too small. There's nothing wrong with adding shrimp and mussels to balance out the diet. I've never tried giving them pellets.
Just feed until the belly is round. 1 or 2 depending on the size should be fine.