Different races respond differently to dearths. Russians, Carniolans and feral survivors in my experience are more likely to shut down than Italians.
Yes, it is so. Some strains continue laying what ever happens.
Bees basic instinct says that if it is short of food flow, slow down or you starve to death.
Then we come to serious issue. If severe dearth continues, bees do not get proper pollen enough for winter bees and lots of hives will die in winter.