What sort of paint is on the walls?
Is it Matt or Silk?
If its matt then the walls will be ok to tile straight onto and as long as the plasterboard isnt damaged and wet and mouldy then it will be strong enough to hold them, if the paint is silk then you should ask the retailer to recommend a suitable adhesive for the job.
the tile adhesive will stick to the paint no problem at all, however a chain is only as strong as it's weakest link. the integrity of the overall bond would be dependant on the strength of the bond between the paint and the plasterboard. if the paint is sound then it 'should' be ok.
personally i'd much prefer to tile on an unpainted background if it's in a wet area. as it would be practically impossible to remove the paint from the plasterboard i'd consider removing the plasterboard and replacing for tile backer board such as hardibacker or aqua panel.
bear in mind that although the paint may appear sound the weight of tiles will expose areas where the paint has not bonded so well, potentially with disastrous consequences.
i may be overcautious but i would prefer to err on the side of caution for such an application.
you may find it possible to overboard without having to remove the existing plasterboard. you'd need to find the joists to fix into and you may find that this technique will build the wall out a bit much - in which case you'd have to remove the existing layer.
if you do decide to tile on top of the paint then do your best to ensure that the paint is as sound as it could be and also give it a good wash down with sugar soap and well rinse. any build up of dirt or grease will drastically reduce the strength of adhesion.
furthermore, in answer to your other question, plasterboard with no finish will bear the weight of 32kg/sqm. a plaster skim will significantly reduce the weight bearing capacity of the plasterboard to 20kg/sqm - i don't know the figure for painted plasterboard but i'd be inclined to assume it to be closer to the lower end.