There can be many reasons why a car surges while idling. Some of these reasons are the computer could be dying, or the fuel injector are giving the engine too much gas.
Is the AC turned on?
There are many reasons why your car might vibrate while it is idling. It could be running too hard for example.
If the car dies while idling, the timing might be off. Other causes can include a clogged fuel filter or a bad spark plug.
IAC (Idel Air Control Valve)
Effectively all the fuel that it burns while idling. You are getting 0 miles per gallon while idling.
No, very doubtful.
Best guess without actually touching the vehicle would be the voltage regulator. on most cars this is part of the alternator. I would start by checking the voltage on the battery while the car is idling and while running ~2000 rpm
Trans fluid is always checked with car level and idling while warmed up.
If your car is shaking while it is idling, it is most likely your automatic choke. The automatic choke is not operating correctly but if you remove the choke and put a lubricant on it, it should stop shaking.
If its computer controlled engine, it more than likely a dirty or bad Idle Air Control Valve.
It is possible it is one of the speed sensors.
Check your vacuum lines this usually the cause for a surge in engine speed when idling or running.