My contractor put in a couple of feet of cement board around the lower tub region, but on the upper half of the tub (shower head portion) he put in drywall. He taped the joint where the drywall and cement board meet. A friend who has done some tiling told me that there could be movement on the joints between the cement board and the drywall, which would cause the grout to fail and start to come out. He also didn't like that drywall was used.
Yes, you should be able to just replace the area of wood that is bad. So assuming that this does not go under the shower, there is no reason to remove it. just cut the bad wood out, back to the center of the joist on either side. Add a couple blocks between the joist at the joints of the sub floor and put down a new piece of plywood.
It should be fine. I would not worry about it. There are going to be joints in the backer board not matter if it is all cement board or not. The joints should be stable as long as the boards are properly screwed to the studs and taped, and as long as you house does not have foundation problems that would cause excessive movement. The main reason for the cement board is in case moisture gets behind the tile. I doubt any moisture will penetrate that high up the wall. It looks like your contractor is doing a good job. Treat him fairly.
That whole area needs to be cement board. There should be NO drywall in the shower area. He took a shortcut to save money. IF you only had a tub that would be fine but with a shower drywall in a NO NO. Make him take out the drywall and install cement board. Even if it was just a tub with no shower he would have had to use green board. Don't let him jack you around with this. It's your bathroom and you want it to last for over 20 years and not just a couple of years. Call your city inspector. Or call the city at 311.
Not like it was done there for a couple reasons. 1st the tile needs to bond to the cement boards at a minimum of six foot in a shower.And a minimum of 5 ft in a tub surround. Going to the ceiling is better , but tile should bond to the cement board if you want it to last. 2nd you should never tape w/ dry wall mud and bond to that. Water will destroy it of time and it will lose its bond.Any taping done at the joint should be done w/ cement board tape and thinset so as the water wont harm it.Any questions you can e mail me thru my avatar and check out my qualifications. Watch out for other short cuts.What thats going to cost him now to redo it is pale in comparison as to the little it would cost to have done it right. GL