The Soviet plans that were formulated and implemented included the invasion of Manchuria, the seizing of the lower half of Sakhalin Island, and the seizing of the Kuriles. Stalin did suggest that they should consider invading Hokkaido, but this was politely rejected by Molotov, who knew the Americans would not tolerate it.

If the war had gone on, would the Japanese have had cause to worry about a Soviet invasion? Maybe, but the logistics of a major invasion, even across a relatively narrow straight (e.g. Sakhalin to Hokkaido) are non-trivial. The Japanese were not aware of the USSR's plans. Even "merely" seizing Manchuria and Korea would have been enough to doom further Japanese war efforts, though, as these were key positions and the source of much imported material.

To get to your other question: the agreement between the US and the USSR was that if the USSR declared war on Japan and began its invasion (into Manchuria) then it would get certain things as a result. These included the whole of Sakhalin and the Kuriles. If the war ended before they could declare war, then they would not get such things. So the timing of the bombs was such so that the US could hope that the war might end before the USSR did these things; the US expected the USSR to begin its invasion in mid-August. As it was, after Hiroshima, Stalin moved up the invasion date, and began the invasion of Manchuria on August 8/9.

Hasegawa's Racing the Enemy covers all of the above well.