When your car run everything should be OK, cause the Alternator generate enough current...
For your idle problem & missing, I would suggest re-grounding the engine, MAF and battery ... (with non permanent wire at first, then see if it make a difference, if so install those GND.
To verify if you really need GND, take a multi-meter, and measure voltage between frame GND, and engine, then MAF, then battery, and see if you read any offset! (check in DC mode, then check in AC, AC will give you the noise measurement, and DC only offset)