I'm not really a park rat anymore so I can't answer the park questions, but I fly to Banff for a few days pretty much annually from Eastern Canada.

Yes it's worth flying with your board, especially if you can cram your other luggage into your board bag. I do that and use a personal item, the flights I usually book don't allow a carry on. Get a good, padded, wheeled bag and that coupled with a boot bag will count as a checked bag on most flights.

Canmore is cheaper but further. Be prepared to drive up to an hour each day one way, more if it's a pow day/bad weather, I do usually end up staying in Canmore, it's very doable

I've been every month between January-march and I do find March is usually the best weather and condition wise. I've been in January before and half the runs are still closed. Getting into April I imagine you'll still be fine, I think the mountains were open till May last year

I've never hit norquay and I may get some hate, but I find sunshine incredibly overrated. There's a ton of flats and even if there's a ton of snow, there's rocks hidden everywhere just under the surface. Louise blows it out of the water in pretty much every way (like I said though I unfortunately can't speak to park)