The problem with your question is that you're essentially asking the historians here to make a value judgement. Historians look to be able to report what happened, and let you the reader decide what your opinion is based on unbiased facts.
There is no right or wrong answer. Whether or not it was justified is a question for philosophy, not history.
It's easy to call any historical opinion you don't agree with as "revisionism," and forget that there is no neutral "baseline" — every historical argument was new at some point. The "orthodox" history of the atomic bomb was largely written by the people who made the bomb, and scholars take it with a grain of salt. This is separate from the fact that some scholars take a very strongly politicized position against that orthodox view. What I've set out below is what I think is a pretty "neutral" set of answers to the questions you've posed.
Hiroshima was a medium-priority target that the USAAF agreed not to conventionally bomb so they could keep a target available for the atomic bomb. It had a military base on it, but was chosen because it was surrounded by a dense urban area. The Target Committee was very explicit about this criteria — the goal was explicitly not to target purely military targets, but to "demonstrate" the bomb's power on a target that would be large enough to see what it did. That meant a city and they were very straightforward about this. Nagasaki was an extremely low-priority target and would not have been bombed at all had not their primary target for that mission, the Kokura Arsenal (again, a nice big military base surrounded by a city) been obscured. Nagasaki had a few war plants in it. Neither Hiroshima or Nagasaki at that point were what I would call "vital to the Japanese war effort" — they were part of the war effort, but the war effort did not depend on either at that point.
The Japanese did not make an offer to surrender but were definitely seeking to determine a diplomatic end of the war, using the Soviet Union as a neutral mediator. They never stated their terms — it didn't progress to that point (the Soviets stalled them). Their main sticking point was the role of the Emperor, not whether he was a deity but whether he would maintain any power at all, or whether he would be tried as a war criminal. The Japanese believed that the character of the Japanese nation required an Emperor and found the possibility of removing the Emperor essentially unacceptable. The Allies knew of this concern and there were many (including Churchill and the Secretary of War) who believed that if the US clarified the Potsdam Declaration to make it clear they would allow the Emperor to retain some role, that it would make the Japanese more willing to accept surrender. Truman and Byrnes overruled them however, largely on the idea that the Japanese needed to grovel. Take that for what you will. In the end the US did decide to allow the Japanese to keep their Emperor in a ceremonial role.
The USA asked the USSR to join in the war against Japan at Yalta, but by the time of Potsdam determined they would rather they weren't part of it. But the USSR was determined to be part of it, in order to get some concessions (notably the Kurils and the entirety of Sakhalin). The USSR invaded Manchuria on midnight August 8/9th and it had a great effect on the Japanese high command. The USSR was not initially planning to invade any of the main Japanese home islands, though Stalin did have some ambitions for occupying Hokkaido (but was discouraged from it by his advisers).
The Japanese high command was split between the die-hard militarists and the "peace" contingent. The "peace" contingent (to which the Emperor and several others belonged) desired finding a diplomatic solution to the end of the war. The militarists thought that the best approach was to try a suicidal "last gasp" that would cause the American public to lose interest in a total occupation of Japan. Much of the maneuvering at the end of the war, and with the USSR in the summer of 1945, was part of attempts of the "peace" party to shift the power around so that there were acceptable ends that did not involve this bloodbath. (Many later studies have argued that they were stymied in this in part by the unrelenting demand for unconditional surrender.)
The Allies knew about the war crimes. I'm not sure what your argument is here, though — because the Japanese did horrible things, the atomic bombs were a suitable form of vengeance? This is a rather slippery ethical and moral road to go down — the civilians killed at Hiroshima and Nagasaki had nothing to do with the Japanese war crimes for the most part. Many of them were children. In fact, elementary schools proved a very useful way to reconstruct mortality rates in the postwar because using attendance records one could estimate how many students were there on the day of the bombing, versus how many survived afterwards.
The invasion casualty projections were debated and debatable but the historical point to be made is that they were not, in fact, a big part of the "decision to use the bomb." There was no real debate or decision and there was no need to invoke such a thing. As for whether an invasion would have happened otherwise, this is not clear. First, I would just point out that making it a question of "do it exactly the way they did it" (two bombs dropped with almost no time in between, on cities) was not the only non-invasion on the table, and second, that there is reason to believe they would have surrendered prior to the invasion anyway, either after the Soviet declaration of war (and there is evidence that even Truman thought they would quickly fold if that happened), or after the months of blockade. The US Strategic Bombing Survey concluded in 1946 that, _"Based on a detailed investigation of all the facts, and supported by the testimony of the surviving Japanese leaders involved, it is the Survey's opinion that certainly prior to 31 December 1945, and in all probability prior to 1 November 1945, Japan would have surrendered even if the atomic bombs had not been dropped, even if Russia had not entered the war, and even if no invasion had been planned or contemplated." You can take that for what you will, but these are not anti-Americans making this statement — they are American military analysts.
As for the "disgusting" situation you point out — the moral argument you are making can lend itself to a "race to the bottom." The moral question of Hiroshima and Nagasaki is independent of the actions of the Japanese in China or towards Allied POWs. They are really quite different questions. There is no reason one cannot condemn both, if one is condemning, say, the purposeful massacre of civilians. If one wants to justify Hiroshima and Nagasaki in moral or ethical terms — a matter on which rational people can intelligently disagree, I think — one cannot do it on the basis of the actions of the Japanese military.
My recommendation: if you are honestly interested in the history, read some of the more recent scholarship on the subject. Hasegawa's Racing the Enemy is very thought-provoking with regards to understanding the Japanese mindset and the role of the Soviet Union and the atomic bomb within that. Ultimately Hasegawa concludes that the bombs probably did not cause the Japanese to surrender, but whether you go down that road with him (I am on the fence), it is a thoughtful and honestly-done piece of scholarship. It will widen your scope.
Secondly, I would recommend reading John Hersey's Hiroshima, and maybe Kurt Vonnegut's Slaughterhouse Five for that matter. You seem to utterly lack empathy with the victims of the bombings. They deserve your consideration. I have no problem with people who want to see the bombings as justified, if they do so using actual facts (and not misconstrued ones, which many people have gotten from many sources that want to tell a very neat and tidy nationalistic tale), and if they do so acknowledging what the targets were and what the damage that was done actually did. It is important to "own up" to the consequences, whether you think they were justified or not. To turn your head from them is just as "disgusting" from a moral standpoint as those who turn their heads from the war crimes perpetuated by the Japanese military — which, I agree with you, also need to be attended to, understood, and taught. A true view of history looks at everything.