I'll take a stab at things...but I'm not an expert.
1. Weight distribution is important, but it's not a hard-and-fast, pass or fail sort of thing. You want sufficient weight on the front axle to have good steering control, and don't want any axle to be overloaded, and want the weight to be as close to balanced side-to-side as possible.
2. Tire PSI is rather important, or more precisely underinflation can be pretty dangerous. It's also fairly important for good tire life to ensure that both tires in a dually pair are at the same pressure (and hence have the same diameter). Different people do have different things they do or do not do for tire care, but the typical basics are maintaining proper/sufficient pressure when driving, avoiding parking on edges or such that the tire is only partly supported, and protecting them from undue exposure to UV light and excessive moisture. Tires are not like fine china that breaks if you look at it cross-eyed.
3. Leveling when stored isn't all that important. Being pretty nearly level when operating an absorption fridge while stationary is rather important for the longevity of the fridge, but the tolerances are more along the lines of "basically pretty level" rather than "laboratory-grade exactly level". If it feels level inside and the cabinet doors don't all swing to the same position and the eggs being fried stay in the middle of the frypan, you're okay. This is not really a concern with a compressor fridge ("residential fridge"), and does not apply when the fridge is not in use. For a residential fridge, you pretty much just need to keep the side with the tires pointing towards the ground.
It probably would be for the best to avoid an extremely off-level storage spot. That is, I wouldn't want to keep my RV parked where the left side is a foot higher than the right or something like that.