1. my 2012 model is a 29690 3naoa
2. not an expert but those varistors look fine.
3. yes, but I would consider gutting it and putting it in a $10 pvc box from menards at that point (when you pick up your 8 gauge and 14-50 socket
Another option is to drill a small hole for the neutral, 18 gauge is probably fine, and connect it to the cut transformer lead, spiral it around the existing cable, and hook it to 14-50 neutral, then silicone the hole, maybe throw a piece of flexable conduit around it while the plug is off.
4. the 4th wire is for neutral. This allows the controller/transformer to run off of 120v while passing 240v through to the vehicle. 240 to the center tap (neutral) = 120. It doesn't have to be large as it is in series with that little transformer (2w?)