I was in a similar situation but with some minor differences, and without getting too far into the weeds or revealing too much information: do whatever he asks, and ask him to clarify and be very intentional in everything. Be polite, be respectful, and most of all be responsive. If obvious whistle-blower type behavior emerges (as in he's obviously breaking the law or violating agreements) then take advantage of your company's means of reporting that. If he does do something that's illegal or near it, respectfully tell him that you don't feel comfortable doing that and ask for alternative ways of doing things that wouldn't require you to make those decisions. If he's spying on you, just accept and ignore it.
Here's what I learned the hard way: guys like that weed themselves out eventually. The lack of competency will surface and become clear to his bosses. The overall goal of the company is to turn a profit and anything that jeopardizes that (illegal/bad behavior, bad press, lost revenue/profit, etc) will be removed. It may not happen as fast as you'd like but it will happen.