Can you tile straight onto plasterboard?
Use a mastic, you'll be ok with a backsplash, not exposed to much water, no weight on the tile. (But this is about the only application I have or would put tile directly on plasterboard.)
If it's flat and clean, no dust just put the mastic on. Mastic is petro based and will self seal. You can't go with tiles over 6x6.
You will have to sand the skim off and get the surface smooth. Make sure you get the right adhesive.