The car not responding is the battery voltage running low and the esc's low voltage protection or low voltage cutoff (LVC) kicking in and protecting the battery. Lipos cannot be run below 3.0volts per cell otherwise damage will occur. To prevent this the esc has a LVC that will reduce power to the motor to let you know the battery is out of juice. If you keep running the car after the esc reduces power, the esc will eventually cut power to the motor completely to protect the battery. As I said before it is completely normal for the battery voltage to rise when you take the battery out of the car and measure the voltage. Battery voltage will drop when throttle is applied and the LVC will kick in during this time. When the battery is out of the car obviously no throttle is being applied so the voltage will be slightly higher.
As as for your motor temps I'm going to say it's because the speed you're geared for is too high. With the 2350kv on 4s geared 16/45 your speed is about 50mph. Your motor will be much happier with a 14t pinion for a top speed around 43mph. If you want to maintain the 50mph top speed you're going to need a bigger motor.
Also while it is possible to run sensored motors in sensorless mode, many sensored motors don't particularly like it. I'm pretty sure it has something to do with the timing and sensored motors liking a bit less timing. If you can lower the timing on your esc that might help a bit and may allow you to run the 15t you mentioned that you had. Either way I'd say 15t is going to be the largest pinion you can run with this motor and it will probably like 14t better.