I'd betcha Stalin knew the date and time and strength of all of our invasions in Europe and the Pacific.
Our hating in the Soviet Union was involved in the development of the Soviet bomb somewhat independently. Much of the espionage at Los Alamos confirmed that the Soviets were on the right path.
As far as the thermonuclear weapon, Sakharov took them directly to the “dry” bomb. Their first was a dry bomb, ahead of our “dry” weapon. The US was still looking at lugging the big Dewar flask based on Ivy Mike.