0. You need to sleep as high as possible for the acclimatization, so you would be better to go for the walk-in camp spots at Whitney Portal just below the trail head. They have never been full.
1. Once you are that high, setting off for the summit need not be before dawn. It should take 4 to 6 hours max to summit from Consultation Lake.
2. Yes, expect lots of snow. You may have trouble finding bare ground to camp on.
3. 20 F bags in a tent should be fine.
4. Saw
one report where the fellow reported a terrible time coming off the summit, postholing forever, and wishing for snow shoes. But that was this month. In a few weeks, about a thousand people will have hiked through the snow before you, so there should be a well-packed cattle trail through the snow.
