Your transmission is an internal failure internally for reverse. It is not fluid and there is no solenoid that controls this. It is a mechanical operation. The transmission either needs to be rebuilt or replaced with a good used unit.
The overheating. Do not ignore the gauge as it may be correct. At this point, you may have a failed head gasket from the overheating. That is where all the air comes from. I would have someone do a leak down test on the system to confirm. It sounds like you have a bad coolant sensor which controls the operation of the cooling fan. Also, if it gets hot at road speed, the radiator may be clogged not allowing circulation.
It sounds like the car is on its last legs, sorry.
Thursday, October 11th, 2018 AT 3:20 AM