Kitchen wall tiling

If the plaster board is completely trashed after removing the tiles your best just removing the plasterboard and rebording the area. The new plasterboard don't need to be skimmed, just prime with an SBR primer. If there is slight damage to the board I would personally fill with rapid fix tile adheisve and smooth with a darby trowel.

It is best practice to remove existing tiles and if necessary re-skim, but that is up to you. I would mark out where cupboards will go and tile so that the cupboards sit over the new tiles, but again this is a choice more than rule.

It is best to remove tiles but if they have been fixed to a plasterboard wall, most of the plasterboard will come away too. It means it is a big job to remove tiles and prepare the wall ready for new tiles. Again, it is best to have a good even surface to fit new tiles to, so skimming damaged walls with plaster is a good idea. You can fit tiles on top of existing tiles. I have done this in some circumstances where it is not apparent this has been done when it is all finished. Regarding cupboards, you can tile around them or remove and tile underneath them. There isn't a hard and fast rule. It depends on what work and to what extent work is being done.