The iFixit youtube video (www.youtube.com/watch?v=KtK7b_pqnCU) shows a method of pulling the adhesive around the bottom, side, and top of the battery. I did this for the first adhesive. The one caution with that approach is that, as you’re pulling the adhesive, it could get caught on surrounding components and that could cause a break if you’re not careful. For the second adhesive I pulled it only in the direction away from the bottom of the phone (as shown in Step 21) and that was MUCH simpler. As you’re pulling the adhesive, even if a slight tear occurs in the process, keep at it with a slow and steady motion to remove as much as you can. Thankfully the adhesive strips came off completely in my repair.
I just completed the battery replacement and I too found that the PH000 did not sit properly in either the 3.2 or 2.2 mm screws. Using a magnifying glass it seemed that the PH000 driver bit did not sufficiently fill the space of the screw. I happen to have the iFixit Pro Kit and used the PH00 driver bit instead, and this seemed to fill the space of both screws much better leading to successful extraction and replacement. My lack of experience with phone repair may have been a factor, but it seemed at least for my particular phone the PH00 was the proper driver bit for these two screws.