Thanks a lot for the detailed tear down description! I was able to repair my keyboard and have no to by a new one. I don know how it can happen, but after a battery change the plastic cap on the end of the battery terminal was flipped around and the battery's positive terminal had no contact with the current collector.
I used two extension bars and a socket of a 1/4" socket set to knock out the battery terminal form the logic board side to the battery load hole without destroying anything. I have not removed the circlip beforehand.
The battery terminal is hold in place by a small heel in the tube. The circlip will clip in when you later push the battery terminal back.
I used a circlip pliers (Hazet 1843a - 12) to squeeze the circlip an bring the whole battery terminal back into the battery tube. I used the same tools to knock in the battery terminal until it latches into its designated position.
About the two parts screw; The upper screw can be removed with a PH 0x50 screw driver. The lower screw is a Torx screw. A T7 Torx crew diver can be uses, but is a bit slack in my opinion.
I recommend to use small multigrip pliers (Hazet 760 N-1) instead of the heat gun to remove the plastic cover. Squeeze the cover from both sides and it will go off without destroying or bending it permanently.