3) What makes you think the US couldn't ramp up production really quickly if they wanted to?
3a) My recollection is the US had originally been planning on a production rate of 3/month by the end of 1945. Obviously, they slowed it down massively with the end of the war, but 20 bombs would be only 7 months production at that rate. If the Soviets WERE stupid enough to go to WWIII over Korea, they'd lose big time, with their nuclear production centres bombed early, and their production would be minuscule.
In 1950, at the beginning of the Korean war, the US had 299 weapons in her stockpile, the Soviets 5.
In 1955, a few years after the end of the war, the US had 2422, the USSR 200
(from
https://en.wikipedia.org/wiki/Historical_nuclear_weapons_stockpiles_and_nuclear_tests_by_country)
The use of a couple of dozen in the Korean War isn't going to affect the US stockpile significantly.