No, not greenboard. I am fairly certain that you want a cement board-type wallboard; Hardibacker or Durock are two biggies (DH used Hardibacker--got it at Home Depot). You also want some sort of waterproofing. Either the Kerdi system (a fabric-like membrane) or a roll-on (Hydroban or Redguard for ex.). None are cheap but well worth the protection.

I have to start with the tub apron itself. I don't like anything that has to do with the picture frame molding on the tub apron. I don't get the frame that runs off the right side of the tub apron and behind the side fo the vanity. I understand that the wall continues off behind the vanity. I just don't get the trim layout and the 1-1/2 frames that cover the tub apron. With that in mind, I'd want the frames on the tub's back wall to mimic, or at least try to relate to, the frames on the tub apron. They don't. Not even close. A single large frame on the back wall. 1-1/2 frames on the tub's apron. To keep the frames on the back wall at a minimum I'd want a chair rail on the left and back tub walls and I'd want to paint the chair rail and everything below it white. Good luck with it.

Does the joint where the glass wall tile meets the deck need a special glass molding? I would prefer none just glass tile to solid surface. You can run the wall tile right to the tub deck, and caulk the intersection with color and texture matched caulk. Borders/liners are added for aesthetic and transitional interest. Sometimes it's purely design, sometimes for function, sometimes a combination. If your glass tile can stand on its own, and you'd prefer it to do so, then let it. I've not ever seen a glass grab bar or hand rail. Clear polycarbonate (I think it was PC) yes, but glass, no. Mongo

Removing the grout was suggested but take a good look at the other grout lines that are not around the tub. I measured them and they're an 1/8th of an inch wide. That's not the case around the tub. Correct me if I'm wrong but I think there should be an 1/8th of an inch grout line between the tub and tile as well. But instead the tile is practically butted right up against the tub (best example is in the first three photos of my original post) resulting in a sliver of a line that's less than 1/16th in some areas. So I'm worried with there being such a small gap that using a oscillating tool may crack the tile or worse, crack the apron of the tub. So now I'm wondering if we should just try to remove the loose cracked grout with a blade of a thin screwdriver, or a 5-in-1 tool, the best we can and then put a bead of silicone caulk over it and be done with it. OR Have the tile around the tube removed and replaced with the proper 1/8th inch gap around the tub and then caulk it. I think the former solution would be the simplest and least costly. Just not sure its the best way. Please advise. Edit: I didn't see the post above from Creative Tile Eastern CT until after I edited my post. I see he agrees that using a oscillating tool is a bad idea.