My contractor enclosed the shower walls with green Sheetrock over the wall studs, then sealed everything with multiple coats of RedGard. Are we able to apply the tile directly to the wall now, or must there be some type of fiberboard used as well?

Need some advice and guidance regarding installing tile on the floor of a small 5' X 5' bathroom. The floor currently has a single piece of good quality vinyl sheet flooring I installed about 15 years ago that is still in perfect condition with no cuts, lumps etc. When I installed it, I first screwed and glued a piece of sanded 1/4" or 5/16" plywood over the 5/8" tongue and groove sub floor so I had a good smooth surface for the install. The vinyl sheet floor was then glued to the plywood where it has remained. So my first question is can I reliably install cement board over the sheet vinyl then install ceramic or porcelain tile on top of the cement board? If so, will 1/4" thick cement board be adequate and what do I need to do to prepare the sheet vinyl floor before installing the cement board. Would appreciate your comments and suggestions. Thank you Dom