The answer is yes. I am not a safety engineer but one of the first things you should think of in an emergency (if the car is out of control) is to shift it into neutral. This will allow you to maintain control of the car and it will let the engine run at a very high speed but you will gain more control over the vehicle. The next option is to turn the key to the off position if there is no other way to stop it. Try to be sure you are near the side of the road when you do this because the car will slow down rather quickly and you may loose the ability of Power Steering which means it will take more of your physical arm power to steer it off to the side of the road.
turn off the a/c and the heater fan
No.
stop it from overheating
My car does NOT do that.
It actually uses less fuel to turn the car off. I just recently found out that Honda is working on an option that automatically shuts the car off when the brake is depressed and comes to a full stop. (red lights)
If by "stop the engine", you mean turn the car off, then the answer is NO!
no
Why would you want to? ----- Try turning off your phone.
Turn the switch off.
Possible vacuum leak
You can stop it from wasting energy by holding the on/off button for 3 sec. and then turning the power completely off.
Your car might turn off when you come to a stop because the car has an electrical problem or a problem with the distributor. It might also turn off when you come to a stop because of a timing issue.