Given that the Japanese were willing to surrender with the condition that the Chrysanthemum Throne be left intact.
Were the Allies right to continue the war and why did Japan end the War.
Was it fear of the Russians as they were afraid of communism or the Americans and their brand of Democracy?
Either way Japanese life was about to change.

It would help if you gave the exact day on which the Japanese informed the US that they were willing to surrender and would also give the dates of what you see as the continuation of the war, please.

The Allies chose a course of action that is considered to have been the only one that would work. The fact that Japan was still clinging to hopes of countering an inevitable invasion, as well as fostering methods by which it would not have to submit to complete surrender, made the decision to keep hammering at Japan the only recourse that would be conclusively effecive.

You have to understand that the Emperor himself was in favor of capitulation, along with a peace faction within the government, and that the main resistance to surrender came mainly from the military factions. The considerations from both sides weren't made with regard to acceding to another form of government for Japan so much as they were based on Japan's deeply rooted history of having never been defeated. The military side found surrender of any form unacceptable, and the peace faction was willing to succumb to the inevitable, but with conditions. There possibly were some considerations given to the tenuous relationship Japan had with Russia as a neutral, but it was more likely the stark reality of complete annihilation of their existence that was needed to force the issue.