No, it’s been proven mathematically. The amount of particulates put into the air will be equivalent of the asteroid that wiped out most life 65 million years ago.
No, it’s left wing drivel.
The actual amount of particulates, their height in the atmosphere, and distribution of particle sizes AND extent of the clouds, depend on a large number of factors which you simply don’t know before the fact.
Number of nukes; dense-pack or not; yield per burst; height above ground vs. ground burst; local weather at the time of detonation and afterwards; and so on.
Learn to think instead of merely repeating “oooh-nukes-scary” pablum BS. You’re among adults here.