My questions are is there a critical mass of bees in relation to stores that it takes to survive winter?
I think you need at least 500 bees to survive winter and insulation if you’re going that small. Colonies that small aren’t going to rapidly expand your colony numbers in the spring though. They might be useful for getting an early start in queen rearing though.
I don’t see many nuc dead outs due to a lack of stores. When I have deadouts it’s usually because they froze. They usually freeze because the volume of bees have gotten too small relative to the volume of the box IMO or they've fallen below that 500 number. I have nucs with only 4 medium frames right now that are going strong. There isn’t a lot of stores in on 4 medium frames. Then again there isn’t a ton of bees in a 4 frame medium box either. It’s a proportional thing. The other problem with “stores” is they are completely worthless if it is too cold in the box for the bees to move around. Hence I am an advocate of well insulated nucs.
Are these overwintered nucs I see discussed different from the nuc I started with in June?
No, these are just nucs that we start in July and August from 2 or 3 frames of bees. They haven’t had time to grow to full sized colonies so we just winter them in their smaller size.
In a slightly different mode, do you try to get the bees to fill up the brood space with honey as the season wears down? If not how much empty comb do you want to see?
Yes, it is desirable to get the bees to fill up a lot of the empty space with stores in the October time frame.
Last, when will the queen start laying again in the spring, is when I see pollen coming in?
Depends upon rather or not the hive has significant pollen stores. If no, then yes the queen will hold off of laying a significant amount of brood until the pollen starts coming in.
is there a temperature (minimum) that I can open the hive and safely inspect without chilling the brood?
I don’t know for sure, but I don’t like to pull frames until it is above 60F and ideally sunny.