Betta

probably, especially if he's one of those nice bettas that play well with others. how big is your tank?

yes, that's too small for cories. they are schoolers so do not feel comfortable if kept alone, so you need room for not just 1 but at least 3 or more.

you can add ghost shrimp, just be prepared that he may try to eat them!

do you have filtration in your tank? how long has the tank been set up? what are your water parameters? shrimp are very sensitive to poor water quality.