Some people believe the strangest things. I cant imagine what harm touching your tires with your hand could do.
As far as tires go, I give them all a thorough inspection for any visual signs of tread separation or nails, screws etc., then I make sure they are all properly inflated before I leave each destination. Also I keep them covered while in storage to limit the amount of sun exposure and avoid premature dry rotting.
Leveling is more a comfort issue than anything else. I prefer to be as level as possible but there's no such thing as 100%. The refrigerator is the only appliance that's sensitive to being level. If you can cook your eggs in the morning without them falling out of one side of the skillet, your good to go for some ! Some prefer the head of their bed higher so they adjust their trailer accordingly, as I was told by one camper.
As far as weight distribution, a larger motorhome would have a heavy enough chassis to handle the average stuff a person hauls around, no matter where it's stored. A small motorhome, may need some consideration as to the proper weight distribution.