Great question. I'll confine my answer to a narrow slice of this: Whether the Soviet Union was ready to respond in kind if it had chosen to answer an American nuclear attack tit-for-tat. The answer is no, the Soviet Union did not have a deployable nuclear weapon ready during the Korean War.
While the Soviet Union tested its first nuclear weapon in 1949, you might consider that test akin to the Americans' July 1945 test in New Mexico: It was not a deployable weapon ready for battlefield use. Michael Gordin's Red Cloud at Dawn is a really good look at this period in Soviet nuclear weaponry. David Holloway's Stalin and the Bomb is another worthwhile source.
Robert Norris, whose work I really trust, shows the growth (and decline) of atomic arsenals in the 20th century. The difficulty of a chart like this is that it illustrates the number of warheads only, not of delivery vehicles. As late as the Cuban Missile Crisis, the Soviet Union had fewer than 50 missiles capable of reaching the United States, and fewer than 200 bombers capable of reaching the United States (and a 2012 Wilson Center lecture makes it clear that it's doubtful that a single one would reach the contiguous states).
During the time of the Korean War, the Soviet Union had not yet weaponized its atomic arsenal in a way that made it "battlefield-friendly" -- for lack of a better term. Not until the latter years of the war did the Soviet Union's atomic weapons graduate from testbeds to something capable of being deployed.
The principal means by which these weapons would be deployed was the Tu-4 bomber, a reverse-engineered copy of the B-29 strategic bomber. This bomber lacked the range to reach the contiguous United States from bases within the Soviet Union proper, and it was believed that most Soviet weapons were deployed in Europe.
It is impossible to say how the Soviet Union would have reacted to an atomic strike in Korea, but it is possible to say that the Soviet Union's ability to respond in kind was limited, if it chose that approach.
I'm sorry, but I don't understand the question. Who is attacking whom?