Yes. I would believe so. I have Acrylic(Glass) block in my shower. This cleaner is strong enough to remove the unwanted but not so strong that it will etch my acrylic block or your glass doors.
Lab tested to be safe for use on: Plastics Metals Decals Painted Surfaces Non-Painted Surfaces Rubber So I would say yes it is.
Yes it will clean them. 25oz of traction wash to one gallon water for heavy cleaning. 12oz to one gallon water for moderate cleaning and 4oz to one gallon of water for everyday cleaning
I cleaned my kitchen with just one application but you might need two depending on how long it has been since the grout was applied. The same would apply to bathroom tile.