I can't say what's best for cories, but I prefer sand - even better what Caribsea sells as cichlid mix (arogonite) which has larger granules.
If you have an HOB, raise your intake or use a prefilter or the sand will mess up your impeller.
Nahhh, unless your intake is literally resting on the sand bed in which case I would wonder why that is....or MAYBE if you're using play sand or something of the like. Most PFS and aquarium sand sold in LFS's won't be a problem unless you have really insane water turbulence throughout the water column (doubt it.)