The US had obviously done many studies to try and estimate what the effects would be. They tested one at the Trinity site in July 1945, and were able to figure out quite a lot from that. Even then, though, blowing up a remote site in the desert is not the same thing as dropping one on a city, so there were many unknowns. But they knew more or less what it would probably do, and how explosive they would probably be.

The Japanese knew of the possibility of atomic bombs but did not think they were going to play a part in WWII. Prior to the dropping of the bomb on Hiroshima they had no idea that atomic bombs had actually been created, much less had contemplated their specific effects.

As for long term effects, the US knew that if you detonate an atomic bomb on the surface, it would create a lot of radioactive contamination. They detonated the bombs far over Hiroshima and Nagasaki, though, and thought there would be very little long-term radiological contamination. However they underestimated how many people would survive the blast and fire effects of the bomb but still be exposed to significant levels of prompt radiation — they were caught off-guard by reports of radiation sickness in survivors.

Starting in late 1945 and continuing up through even the present period, the US has helped fund research into the long-term radiological effects of the bombs and has learned that it is in fact quite a complex scientific problem, far more complex than they knew at the time.