When I convert an existing room into my new master bath, should I remove all the drywall before putting up the special drywall for bathrooms? Can the new go up over the drywall?

Not a good idea at all to go over the old wall with new. Bathrooms only need greenboard or blue board in damp areas not the whole bath but normally worth doing. Wet areas need more protectionwith cement board, wonderboard, hardienoard, etc...