i know of two very good horses who have been injured on Treadmills and would not advise it.. Both used it sucessfully many times but were injured badly. Both were on it to test respiratory rates and blood pressure and temp... all things which could have been tested on the lunge, ridden.
Not sure on that front.. To be fair, they probably have back up generators on there treadmills and are probably more modern than the one i have had experience with.
You'll be fine - they do it all the time - clinically and for research. if it's for an endoscopy then i presume he has breathing trouble? it needs to be done on the treadmill to use all the equipment.
They can take pictures etc and view what happens as the horse is working at full exertion or with endurance.