* how much snow might be there in late November?
You should know snowfall is highly variable in the Sierra. A storm can dump 3' or there can be nothing at all.
* if the road ever closes in winter?
Yes, all Sierra roads up high can close. Check with the USFS in Bridgeport for the latest conditions.
* if there's typically any avalanche danger?
I heard of a big slide up above the Twin Lakes Road that swept two guys in their truck about 100' into Twin Lakes. They didn't find them till Spring. I was skiing Matterhorn in May when a small slide crossed our tracks. Plenty of hazardous terrain everywhere.
* if the snow in late November typically makes it a crampon/snowshoe trip or if it's simply an awkward in-between time (perhaps earlier is better for climbing and later is better for skiing).
New or even old snow isn't like ice. Usually the worse it gets is crusty snow, though I have seen bubble ice in the Northern Sierra, after a period of drought and enough sun to melt the upper layers. Cold storms bring powder, and then the sun can turn it to junk skiing. Most people don't climb or ski till spring.