P0128 is generally a stuck open thermostat, or the sensor as you already know.
If the temp needle doesnt get to 12 o'clock and stays a little on the left of the 12 o'clock position even after the car is fully warmed up(about 5 minutes of driving) that means the thermostat is stuck open and the coolant is going through the pipes all the time.
Since you are already doing the pump, thermostat and the tank, do the hoses as well. Hoses are cheap and the earliest point of failure.
Upper hose is super easy, the lower one is a little tricky. It houses the sensor too. It would be a good idea to get that sensor replaced as well as you will already be there.
As for AC whacking out, I dont think it is related to the P0128 code. When the thermostat is stuck open, the heater does take time to blow full heat though.
What does the OBC read about the ambient temperature? Most of the times its the temp sensor(in the driver's side fender well) that craps out. If it is reading normal, then may be FSR or something else.
I am not very familiar with the AC system, but P0128 definitely. I had the same code and changed the thermostat and the hoses.
Doing coolant flush and water pump pulley soon.