the engine to stall and surge at idle
It shouldn't. When the engine is running, electricity is supplied by the alternator, not the battery. If the engine dies when the battery is disconnected, the battery and/or some related part (such as the voltage regulator) is bad.
A bad IAC (idle air control)or vacuum leak. Check for bad vacuum hoses first, the IAC is around $50
bad IAC
possible bad TPS, IAC, or ECT sensors
probably bad TPS, or IAC sensors
probably got a bad IAC motor
Get engine running. While the engine is running disconect the POSITIVE termninal from the battery. If the engine dies, the Alterntor is bad.
If you unplug sensor and one or both fans come on.
Start the car, unplug the battery the alternater should power the car. If it dies the alternator is bad. You can also get it checked at any parts store.
Your motor will idle badly. The revs will not stay at a constant level, even when your engine has reached operating temperature. ***Sum's Answer***- the engine will idle bad, and it wont catch its idle when droping RPM's. It may drop to 500rpm, shoot back up to 1k then slowly figure its way out to 6000-800rpm. Overall, it will idle badly, and not know where its going. It may not be your IAC motor though, I had that problem in my 03' Cavalier and it wasnt the IAC, it needed a computer update.
Sometimes your engine rpm will rise on it's on. It will sound like the ANTIQUE-STYLE OOOGAH HORN