Soviet union doesn't declare war on Japan

[sillygoose]

Did the Japanese try to surrender on terms that were actually acceptable to the West?

IIRC they were the terms they ultimately surrendered under.

BTW, I wish that the Potsdam Declaration would have contained something about the fate of the Japanese imperial system, but I don't know just how politically feasible that actually was, unfortunately.

Probably not the time nor place for it.

Is it true that the Soviet advance into Manchuria was running out of steam when the US nuked Japan twice?

Yes it had run into a bunch of logistical problems due to being launched before they were ready to gain surprise.