bathroom waterproofing
Like most things in life, there's multiple answers.
The best option for a direct water contact surface is water impervious backer board.  This is typically used in shower walls, or behind tiles that will have direct water contact.  Even this excellent material can fail if installed improperly.  The extra strength permits it to hold tile easily, with proper bonding.
Non-water impervious backer board should be avoided for areas with direct water contact, for obvious reasons.  It is suitable for areas that will need to hold the extra weight of tile but aren't in direct water contact.
The &quot;green&quot; water resistant drywall can also be used where there is direct water contact.  I've seen a mix of good and bad installations with this material.  Some people love it, some think it's not as good as water-impervious backer board.  It is easier to damage, and can't hold as much weight as backer board.
Non-water resistant drywall can be used in the bathroom too, but limit it to areas not likely to encounter much (if any) direct water contact.  Mist and steam contact will be OK, provided you properly sealed the drywall with paints that block water vapors.
Yes, it's possible to have a cupboard in the bathroom.  Many of them have standard cabinets.  Again, you can upgrade the cabinets with custom cabinets if you are worried about direct water exposure.  A good bathroom floor plan tends to have the wet areas isolated from the cabinetry, preventing water from routinely getting under the cabinet.
If you are new to this kind of rework, to get into the details I would recommend getting a copy of &lt;a href=https://www.amazon.com/Renovation-5th-Completely-Revised-Updated/dp/1631869590&quot;&gt;Rennovations  Often reading through it will help you with questions like this; but more importantly, you'll also notice the other related steps, which will reduce the chance that something you didn't even consider becomes a problem in your home-building plans.