Just a quick thought on your other issue of your RPMs dropping even when the car does not die. If the car is cold, the engine/ECU will keep the idle a bit higher than normal to help warm the engine up quicker. This happens to me every day, I let the car idle until it drops down to normal idle RPMs, generally about a minute. The RPMs usually go from about 1200 to about 700 in P, then once warm the idle when fully stopped and the car in drive is about 500...

just a quick $.02.