I'm remodeling both bathrooms and I'm installing vinyl walls in the shower and around the tub in a mobile home. Is it necessary to have cement board or green board or dry wall behind this and should cement board be used on the ceiling above shower and tub.

Cement board is used as a sub for wet areas that get water contact regularly. Cement of te ceiling is not necessary but its OK if you want to and plan to tile. Were you tiling the ceiling?