I think you can definitely make a rule about open flames. I'm pagan and we (general we) love, love, love our candles
but there is no absolute requirement that we use them. Many of us, myself included, have "made do" in places where we couldn't set up an altar or couldn't burn things, etc. If all else fails, one can meditate and visualize it. I think you can rightfully govern his outward
actions (such as burning things) if you are concerned about their possible effects on the household.
I don't think you can really govern his inward
thoughts and actions. If he is this religion, he is going to be this religion in his head, and even if he doesn't have the trappings to do a big bells-and-whistles ritual of his religion, he will still most likely be doing quiet prayer, and I don't think there's anything you can really do about that as long as you're willing to have him in the house in the first place. Basically, if you don't even want his god(s) prayed to silently in your house, you should probably find him another place to stay--but if you're OK with quiet prayer, I think you can ask him not to add a bonfire and a drumming circle to it while he's there.
Basically, I agree with MorgnsGrl.