No, it would not. There are many things that could cause a stall at idle. The throttle plate could be dirty as well as the mass air flow sensor. You did not mention the kind of car or engine size. Is the check engine light on, is it when the engine is warmed up or cold?
It would depend on what vehicle you have but generally it is located very close to the thermostat housing in most vehicles.
The length of time that a battery would last in a Toyota Camry would depend on many factors. The amount of miles the vehicle is driven would be one factor. Another would be the outside temperature. The battery will last longer in warmer weather than colder weather.
That would depend on which temeprature sensor you are asking about. Is it the coolant temperature sensor or the air charge tenerature sensor you are asking about?
It would help to know the sensor that needs resetting.
Coolant Temperature Sensor
It would depend on the vehicle. most likely the vehicle would run, but not well. this puts the computer in limp home mode. most car computers will allow the vehicle to run with one major sensor undone.
Code P0113 indicates a intake air temperature sensor circuit high output. Check the connection to the intake air temperature sensor and if that is fine consider replacing the intake air temperature sensor.
A TPS is normally known as a "throttle positioning sensor" price would be dependant on the vehicle.
The vehicle would run on battery power until the battery runs out of power.
The battery is dead - you would need to boost the vehicle in order for it to start , but once you shut the vehicle off it will not start again without boosting or hooking it up to a battery charger
To help you turn your backup sensor on I would need more information. What does the backup sensor go on? What type of vehicle? What year is it? an what model vehicle is it?
The temperature of the water will vary on any vehicle with speed, including on the Taurus. The more an engine runs, the higher the water temperature will be in the radiator. If the radiator is overheating, then there could be a malfunction with a temperature sensor, a leaky hose, or damage to the radiator.