Tile straight onto the plasterboard and dont seal it with anything, as for the painted walls ye just rub them down and tile straight on. I sometimes use "Thistle bond it" Its kind of a gritty sealant that you roll on to shiny surfaces to form a key. I'm not a tiler I'm a plasterer but thats what I would do.
no debate to be had here - plasterboard should NOT be sealed. it is engineered to be a finished substrate ready to take whatever is going onto it.
personally i'd try to remove the paint, you can tile on it if it's sound though you are asking for the paint to bear the weight of the tiles. whichever you do you will need to seal with a tiler's primer, either latex (SBR) or acrylic based. don't use PVA.
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