Re: battery Draining
Well, maybe I'm not familiar enough with late model computer controlled engines, but I'd ask how the battery is involved with missing and stalling at idle.
The battery is used to start the engine. Once started, the engine runs off the alternator, and the alt charges the battery. Therefore, if the battery consistently starts the car, its not a battery drain problem.
Since the alt typically produces less voltage at idle, you may have a problem with grounds or connections to the various electrical items involved with running the engine, such as the computer. The computers hate bad connections, low voltage, etc.
Get a decent DVM and check the battery voltage with the engine off, and engine running. 12.6VDC off and at least a few Volts higher running. The Voltage should go even higher as RPM increases.
From here it gets into troubleshooting the electronics and sensors, which can be fun.