Cories need to be in groups of four or more and since that is to much bioload for a five gallon need a larger tank. You can't really do any other fish. Nerite snails rarely lay eggs and their eggs won't hatch in freshwater, if that helps.
Yup they sure do. So far I've been successful with avoiding eggs by just getting one of each kind but I bought them from a store tank where there weren't too many of the same kind.
Not any invisible algae types I know of. Never really had success feeding them wafers either. Usually fish and pest snails got to them first. In my experience they really do best on real algae. Even just a little bit will do.