There are many nuances here (unfortunately not captured by the comment of /u/NateJL89 , which reads as a "hard orthodox" interpretation which is also not supported by historians).
In the spring and summer of 1945, there were elements within the Japanese high command that were probing the options for a mediated, conditional surrender. The Emperor himself authorized various entreaties with the then-neutral Soviet Union, in an attempt to see if they might possibly serve as a mediator with the other Allied powers. The goal was to find a way to end the war without sacrificing the state of the Imperial House, and to perhaps gain some kind of basic concessions. These entreaties occurred in both Moscow (with the Japanese ambassador to the USSR) and Tokyo (with the Soviet ambassador to Japan).
These attempts were not successful. The Soviet Union had already committed itself to entering the war against the Japanese and were looking forward to gaining strategic territory in the Far East as a consequence of that. The Soviets strung them along, knowing they would soon turn on them.
The United States knew about these attempts both because the Soviets told them about them, and because the USA was at that point capable of tapping into Japanese foreign cables and decrypting their contents. The MAGIC intelligence files were correctly interpreted by American analysts as a sign that there were elements within the Japanese high command seeking a conditional surrender, and that they understood that the main sticking-point was the state of the Imperial House (the Japanese felt that to allow the Allies to dispose of the Emperor — or even keep that as a possibility — was too much to accept).
It should be emphasized that the Japanese military heads were not in favor of a mediated solution. So it was not a simple thing as the Japanese being "ready to surrender." But one can say, there were elements within the Japanese high command, including the Emperor, who were trying to find a diplomatic resolution to the war. The United States knew of this. Of note is that President Truman and Secretary of state Byrnes did deliberately avoid pandering to those elements — against the recommendation of many other advisors (including the Secretary of War and Churchill), who thought that clarifying the Allied position on the Emperor would make the acceptance of surrender much more likely. So there is some evidence to support the idea that Truman in particular did not use every option at his disposal when it came to seeking a surrender as early as possible, and indeed it was a common postwar critique (not by left-wing "revisionists" but by military officers) that the United States' insistence on "unconditional surrender" may have prolonged the war.
All of this is nuanced. There are some people who want to say that the bomb was used entirely unnecessarily, and there are others who want to say it had to be used exactly the way things occurred. Most historians are somewhere in the middle on this. I have written something of an overview of different arguments here, with some nice citations to historiographic essays by J. Samuel Walker that emphasize the shared middle-ground between these extreme interpretations. For a single volume that does a good job of talking about the Japanese "peace feelers," and what they did and did not say, Hasegawa's Racing the Enemy is good.
No. This theory is often found in the work of Gar Alperovitz, who claims that the US only dropped the atomic bombs to to impress the Soviet Union with their might. The US hoped, he argued, that this would give them the upper hand in foreign policy in the post-war period. However, Alperovitz relies on deceitful scholarship to prove his point, ignoring evidence or using ellipses to make quotes from government officials serve his thesis. You can find his work debunked in the edited volume by Robert James Maddox, Hiroshima in History: The Myths of Revisionism.
Other evidence goes against this, such as Truman not using the bomb as leverage in negotiations over Poland, which the US handed to the Soviets after the first successful test. Moreover, if the Japanese were ready to surrender, why did Truman, at the Potsdam Conference, get reassurance from Stalin that they would help them invade Japan? This went against US interests, and the Soviet invasion of Manchuria and their subsequent aid to the Chinese communists there helped them in their fight against the US-backed KMT.
Some people argue that if the US had only not insisted on an unconditional surrender, then the Japanese would have surrendered right away. Perhaps, but it might be interpreted as the Americans losing their will to invade, which Japan could exploit for a better bargaining position. However, the Japanese government was not a unified entity. Their was a split between the military and civilian governments, and the military was calling the shots at this point. Some Japanese officials did send out feelers to the Soviets indicating their willingness to negotiate - not surrender. However, there are other diplomatic cables the Americans had decoded at the time that contradict these. After the war, many high-level military officials, like Toyoa Soemu, Nagano Osami, Suzuki Kantaro, and Koichi Kido testified that it was the position of the Japanese leadership to continue fighting in order to get better terms of surrender. Indeed, even after the bombing of Nagasaki, Army Minister Anami, wanted voluntary disarmament, no military occupation, and Japanese control of war crimes trials before a surrender. In the end, they did not get these, of course.