It is known that the US tried to justify their atomic bombing of Japanese cities by claiming they were aimed at military targets such as a plant and a bridge. Yet the bombs destroyed much more than just a plant and a bridge - virtually, the whole cities. The human life loss much exceeded the numbers of the plant's personnel.
Did the US indeed expect that the explosion will destroy just one factory rather than the entire city?
Your definition of "military target" is incorrect. The entire cities WERE military targets because military installations and arms factories/storage facilities were located inside the city limits.
Quite apart from that, the policy of carpet bombing cities was well established at the time and was being performed on a daily basis by B-29s carrying conventional explosives and firebombs.
The effects of such bombing on the population were known too, at least in estimate, based on figures attained from German bombing on English cities and analysis of damage done to German cities.
So no, the expected casualty count was well known, and was not expected to be much different from using the standard system of firebombing the same cities. The reason the nuclear weapons were chosen were mainly
In addition, a surrender at this stage would stop the war before the USSR could launch a major invasion into northern Japan, AND would make the US invasion of Japan scheduled for the spring of 1946 unnecessary, preventing an estimated million US and 2-3 million Japanese casualties just from that.
http://en.wikipedia.org/wiki/Operation_Downfall has some information on casualty estimates (note, the half a million US casualties listed are deaths only, include wounded and a million is low). https://www.mtholyoke.edu/acad/intrel/giangrec.htm has more.
Based on a cursory reading, I don't believe the United States underestimated the death toll. The bomb itself was known to be devastating. Einstein himself petitioned the government to with hold the use of the bomb, knowing full well that the weapon was many orders of magnitude more dangerous than any sort of conventional bombing technique used up to that point.
You can see in both the crewman's account and in the Potsdam declaration, that the United States had foreseen the affect of the bombing, "utter destruction" and "utter devastation", "an act of war to end the war." The Americans knew what they were doing and they knew the death toll with be staggering. They weren't intending to hit a bridge or a road. They were trying to disable the Japanese completely. The stakes were so high that they were willing to sacrifice any number of people to end the war.
In short, no, the Americans didn't overestimate or underestimate they simply gambled that it would do what was needed. And in that at least, they were correct.
Crewman's account of the bombing
I'm going to hedge the above claim by pointing you to this. It's well sourced and seems to be relatively contradictory to my statements.
This is not a complete answer, but it's too lengthy for a comment.
Did the US indeed expect that the explosion will destroy just one factory rather than the entire city?
No, they intended to destroy the whole cities. The idea was to make an overwhelming show of force in order to accelerate a Japanese surrender and convince the Japanese to surrender unconditionally rather than conditionally. It was unclear whether the Japanese could have been forced to surrender without an invasion, which would have been very bloody. Some historians have also interpreted the bombings as a prelude to the Cold War; by using them, the U.S. gained strength in its postward struggle with the USSR to carve up the world into spheres of influence.
Was the death toll in the atomic bombing of Japanese territory greater than was expected by the US?
They certainly expected to kill a vast number of civilians, but there were a variety of factors that probably made it impossible to make accurate numerical estimates of the number of civilian deaths:
The cities had been partially depopulated because there were food shortages, and many children had been sent out into the country, where there was food. I doubt that the US had accurate information on the exact number of civilians remaining in the cities.
Many of the deaths would have been from fires as the cities burned. This seems like it would be impossible to predict.
In 1945, knowledge of the effects of radiation on humans was pretty rudimentary. At Hiroshima and Nagasaki, there were people who survived the initial blast and were exposed to radiation. Their doses depended on factors such as how far they were from the blast. There were smaller numbers of people with larger doses, and larger numbers with smaller doses. The effects of small doses of ionizing radiation are not well understood today, and were certainly not well understood in 1945. Attempts to retroactively estimate the effects have been hampered by the fact that when a city burns, a lot of nasty carcinogens are released into the air. (This was a problem after 9/11 as well.) There is evidence that very small doses of ionizing radiation can be beneficial, an effect called radiation hormesis.
There is a paper on the radiation stuff that you can find online (in English): M. Mine et al., "Mortality of A-bomb Survivors in Nagasaki and Hiroshima."
You are confusing the aiming point with the target city.
Hiroshima was the headquarters of the division of the Japanese Army tasked with defending Kyushu. There were more than 50,000 troops quartered in that city. It had a number of rivers which made the city unsuitable for conventional carpet bombing. There are very few T-shaped bridges in the world, making that landmark rather unique and hard to mistake with any other city.
Kokura was the primary target for the 2nd atomic bomb. Due to overcast skies, the navigator was unable to determine that they were over their target, or even over land. This city used to be called Kokura Arsenal due to the number of munitions factories.
Hiroshima was a huge natural port. Historically it was the only port open to foreigners. In the event of a conventional land invasion, it would be necessary to take and hold this port so that Allied shipping could use it to land troops and materiel. This invasion was called Operation Olympic and was scheduled for November 1, 1945.
