Originally Posted by SilberGrauE60

you may have a bad alternator or loose accessory belt, not supplying enough charging voltage during operation. Otherwise, the alternator should keep the car operating normally when the engine is running.

Also, on your second question about the parking lights: You must have bumped the turn signal lever upon getting out after the car is shut off. This sets the European marker light function--one side illumated only. Up on the lever sets the right side lights, down sets the left side. This is supposed to make your car visible when parked on darkened streets.