April / May and September / October are both bad for Alaska for different reasons, April and May will be snow melt, slush season for much of the state. September / October is the rainy season, and the beginning of the winter storm season. We went to Alaska on a non-rv trip about a decade ago in late September, and did not see the sun for a week, it rained almost every day, and much of the tourist industry was in the process of shutting down for the season, I suspect October is even worse. If i had to pick any of these months it would be May.
Now down to your questions:
1, Most RV's are not designed for winter use, they are poorly insulated, often have exposed plumbing which can freeze, etc. There are some models that are slightly better insulated, have enclosed heated tanks, etc. Even such "4 seasons" models will be a challenge at temperatures below about 10F / -12C, my coach is a 4 seasons model, the coldest weather I have used it in is 12F /-11C, just one night at these temperatures with the wind howling burned as much propane as I normally would use in 3-4 days with temperatures around freezing at night, and had the propane furnace running over 50% of the night. Even this left my tank dump valves frozen the next morning.
2, I am sure some RV's use winter tires in the northern states, but it is not a thing where I live. Be aware a number of the western mountain states require all larger vehicles to carry snow chains or snow socks in the cooler months, typically October - May, this is required even if you don't use them. Exact terms of such laws, if they apply to private vs commercial vehicles, etc. varies from state to state.
3, I am not sure about this one, however be aware most Class C's are designed to maximize the number of "sleeping" spaces at the expense of everything else, and often have less cargo capacity than a similar length class A. A 30 ft long Class C will typically be built on a 12,500 or 14,500 GVWR (gross vehicle weight rated) chassis, where a similar 30 ft long Class A coach will be built on 16,000 to 22,000 GVWR chassis, the heavier Class A chassis will allow for heavier / sturdier components, more cargo compartments, possibly higher cargo carrying capacity, etc. Though of course there are some practical exceptions to this rule. Super C's built on commercial truck chassis can be even higher, but they tend to be 34 ft or longer.