Actually, the news of Hitler's death was released throughout Germany between May 1 and May 2 and the final surrender of Germany didn't occur until the 7th and 8th. The Germans did keep fighting after Hitler's death but by this point everyone knew what the end was going to be; the majority of Germans were simply fighting to give the civilian population enough time to escape the Russians.

I really doubt this. Even though he won the war (at least that's how his propaganda teams characterized it), Stalin's memory was quickly reviled even in the Soviet Union only a few years after his death. There was little love for Stalin in the Soviet Union; tons of fear and respect but little love. His end would have been very different from Hitler's, as the latter was still revered by many Germans even years after the end of the war, when it was known how devastating his rule had been both for Germans, Jews and the rest of the world.

One way I think this what if scenario could be envisioned is if some high level Soviet official decided to use Stalin as a bargaining chip in negotiations with Germany and seized him. Would Stalin's bodyguard have allowed this and followed the coup or would they have defended their leader with their own lives? I can't say as I don't know enough about the personal security detail attached to Stalin.

What would Hitler have done with Stalin? This would have been an enormous propaganda coup so I'm sure there would have been film made of the captured leader and shown on newsreels. Whether Stalin would have been dead or alive in the film, I'm not sure.