The absolute wanted to test the bomb on a live city. That’s why they didn’t fire bomb Hiroshima and Nagasaki like they did Tokyo. It also acted as a way to threaten the Soviets/rest of the world.

You are absolutely right that they wanted an unconditional surrender. I believe it was during Tehran Conference that the west agreed to not sign a peace with Nazi German once we beat them back to the French/German border.

The Second World War was all about enshrining the establishment. Just look up the "Four Policemen".