Forgive me for not explaining myself properly - you tile the back of the door.
You can make it so that it's a push fit - it's not difficult. Mine's like that.
Anyway, it sounds as though you're against the idea - you could just fit it as it is. Most faux wood panels are of the same construction as wardrobe doors anyway. Having said that, they do split when they get wet.
For painting, it depends on what sort of finish you want - if you want to keep it looking like wood, you could probably get away with varnishing it. If you want to paint it (successfully), you'll need to give it a coat of decent primer (zinser 1-2-3 or Dulux supergrip) first then paint it with what you like. These primers are expensive though.