Installing tile over painted sheetrock
Hi there,Sorry it took so long to get you an answer----
No to all of your questions.
Drywall and green board are not allowed in a wet area, I recommend Durrock.
Use a modified thimset (powdered--you will need to mix it with a drill)
Even the best grouts are not 'waterproof' moisture will get through in tiny amounts.
Epoxy grouts are the closest thing to waterproof--however a house moves a bit throughout the year and tiny cracks can appear over the years.