I think the first bomb was a test. The second being real.
Nope! They actually tested the plutonium bomb before they dropped the bombs on japan. They knew the uranium bomb would work, but the plutonium bomb and its yield was a question. It was more destructive than they expected.
Would a conditional surrender have worked? Technically, the japanese DID do a conditional surrender, but it was so far along the lines of our unconditional surrender that we allowed it. There is no doubt that japan is enjoying more prosperity now than it has ever enjoyed in the past. Had we just won and left, they would have been taken over after a few years by china.
One other nice question to ask is: was it wrong for the americans to insist on full demilitarization and then build their economy up from the ruins after the war? Then we can go into korea and question our motives there.
People tend to get stupid when it comes to nuclear. Chemicals, nerve gas and biological agents have all been used against civilian and military targets for appauling effects. Fire has killed billions since it was discovered as an effective weapon. 2 bombs were dropped 65 years ago and NONE have been needed as weapons since. Really, the best weapon is one that you never really have to use. If we built a laser cannon in orbit and used it to cook a couple middle east cities then people would question if we /really/ needed to do that as well. Would they then persecute all laser cannons? Probably not. Why? Because nuclear stuff requires you to be really smart to understand it. It's easy to point as something you don't understand and call it 'the devil'. Most people don't understand lasers yet either, but we have yet to develop laser weapons that take out cities.
The fact is, history is history. If one day we can eventually travel back into the past, I would caution against trying to change decisions like this, or even some of the more heinous war crimes. Such events may cause unexpected consequences and ultimately lead to the planets early demise.