1-if it's carbureted, it likely has a clogged slow jet (from sitting for 2 years with ethanol-laced fuel) preventing it from idling.
2-that headlight beam is run off AC current so it only comes on when the alternator is turning (i.e. when the motor is spinning the alternator fast enough to generate AC current).
Remove the carb, remove and clean the jet, making sure you can see light through it when you are done. The headlight is not a problem.