Can it be used mounted to a shotgun

electrical tape

I don't see why not. They make stiff rubber universal mounts that should accommodate the shotgun and the light.

same mount that comes with it that mounts it to the scope should mount it to shotgun.

thats what I think also

Yes. It's cool because waterfowl hold absolutely still when illuminated at night.

Yes, it can. I mount mine to my shottie often. The best part is at less than 30 yards if the animal is in the spotlight then you are already on target! Just squeeze the trigger.