If you're talking about cories for your catfish (which it sounds like you are), then he should be fine with them. My girls completely ignore their cories, except Rosalie who makes sure they're all doing their jobs. I'd worry about the betta harrassing the ghost shrimp, but they should be okay.
if you provide some thick plants (artificial or real) for the shrimp, It should be okay, as long as your catfish stay at the bottom mostly and arent colorful ( which most catfish arent)
snails reproduce quickly.. i would only get one snail unless you want to become overrun very very quickly. Cory catfish should only be kept in groups of 4 or more so if you have the room I'd say go for it (they get along with my male and female bettas because they are very peaceful yet active fish). Im not sure about the shrimp, but my betta LOVES baby brine shrimp so id assume that if they are small enough to fit in the bettas mouth then they will end up there. Dont forget to add your fish slowly (say over the weekend not only for your tank but for the betta too. We dont want any stressed out fish!