Short answers, pulled from the story.
Japan's surrender was announced by Emperor Hirohito on the 15th of August 1945 and formally signed on the 2nd of September 1945, aboard a U.S. Navy battleship in Tokyo Bay. The state of war with the Allied powers did not formally end until the Treaty of San Francisco came into force on the 28th of April 1952.
The Potsdam Declaration was issued on the 26th of July 1945 by the United States, Britain, and China, demanding Japan's unconditional surrender and warning of "prompt and utter destruction" if Japan refused. Prime Minister Suzuki publicly used the word mokusatsu -- meaning anything from "refusing to comment" to "ignoring with contempt" -- which the Allies interpreted as outright rejection.
The Soviet Union had secretly committed at the Tehran Conference in 1943 and the Yalta Conference in February 1945 to enter the war against Japan within three months of Germany's defeat, in exchange for substantial territorial concessions from the United States. On the 9th of August 1945, the Soviet Union declared war and launched an invasion of Manchuria, shattering Japan's hope that Moscow would broker a negotiated peace.
Emperor Hirohito broke a 3-3 deadlock among the Big Six just before midnight on the 9th of August 1945, personally sanctioning acceptance of the Potsdam Declaration. He repeated this decision on the 14th of August after Anami, Toyoda, and Umezu made a final case for fighting on, and recorded the surrender broadcast that aired on the 15th of August.
Major Kenji Hatanaka led a coup attempt on the night of the 14th to the 15th of August 1945, aimed at seizing the Emperor's recorded surrender address and preventing its broadcast. Hatanaka killed Lt. Gen. Takeshi Mori when he refused to join, but was unable to find the record, which had been hidden by court chamberlain Yoshihiro Tokugawa. The coup collapsed when Eastern District Army commander Shizuichi Tanaka ordered the conspirators to stand down at dawn.
Operation Ketsugō was Japan's plan to defend Kyushu against the anticipated Allied invasion, staking everything on the beachhead rather than defense in depth. It called for more than 3,000 kamikazes in the first wave, followed by 3,500 more kamikazes, 5,000 Shin'yo suicide motorboats, and the remaining naval fleet. The strategy depended entirely on Soviet neutrality, which collapsed when the Soviet Union declared war on the 9th of August 1945.