I don't really see why Max would need to minimize his trips up and down the stairs. That's the egress to his apartment and cooking out on the grill is a reasonable use of the property he has rented.
As far as whether or not his meat is covered, also, its no one else's business. If Kevin doesn't like it he doesn't have to stand in the hallway while Max walks by.
I don't think Max has to cut out his trips up and down the stairs, but I do think he should minimize the impact of those trips on Kevin.
There's necessary noises of daily living--people walk on their floors, flush the toilet, run the dishwasher, watch TV, talk, etc. You can't really complain about them, because there's nothing anyone can do about them. And there are the noises that can be controlled to some extent--slamming doors, loud volumes on TVs and stereos, yelling, wearing hardsoled shoes indoors. Those noises are far more irritating, because you know they can be controlled, but the other tenants simply don't care to.
It's possible that the stairs are carpeted and Kevin hears nothing when people are walking up and down stairs, and that the front door closes silently, instead of banging shut, and that Max never talks loudly enough to be heard in Kevin's apartment.
But I'll bet the reality is that Kevin can hear footsteps and the door shutting and Max talking on the stairs or out on the front lawn. In a shared living situation like this, I think the polite thing to do is to minimize the impact these normal noises of daily living have on the occupants of the other units in your building.
For example, due to some medical issues, I have to wear shoes all the time. I also have downstairs neighbors. So I wear Keds in the house, which don't make noise when I walk, and I have area rugs down over most of the floors. I use headphones when I watch TV, because I like to turn the volume up. I'm very careful how I shut the outside doors early in the morning or late in the evening, because someone could be asleep. I don't slam the doors, ever, unlike the downstairs people who slam, slam, slam all day long.
So if Max is disturbing Kevin with every trip up and down the stairs, while he doesn't *have* to do anything, it would be polite and neighborly to reduce the number of trips if possible, and to do everything else possible to reduce the noise associated with the trips.