Hanging vertical tile in powder room, cement board or drywall?
I am generally apprehensive about fixing tile directly to gypsum wallboard, and recommend using cement board if you have the choice. It is imperative that you do not use wallboard in a wet location.
That being said, I have seen tile attached to wallboard work perfectly well in locations with low moisture and where any rough use (impact) is not likely.
As for the stud arrangement and attaching the wallboard, I would consider it mandatory that all the edges are supported with wood.