What an interesing topic. Now tracking!
Stalemate

those stalemates were all done on april fools day at some silly tournament foolish enough to play on such a fine day.

10 moves? This is the fastest I thought of by myself:

not a stalemate,just a draw because of 3 move repitition
The criteria for draw by repetition is triple repetition of position not move. So in the game given, the draw is claimable after move 4.

Checkmate in 1 move- for white and black.
I can't see any for black but can for white.

Checkmate in 1 move- for white and black.
I can't see any for black but can for white.
Black can play Nxb6#, but it's not forced.

I've just realized that I am an idiot.
. . .
Oh yeah. Somebody should have realized this long ago.
And the fastest double stalemate (getting closer to the creative theme first started in this posting) -
By Minerva:
Wow, 18 moves! That's genius. Do you know if this is the fastest double stalemate possible, or just the fastest yet discovered?
Checkmate in 1 move- for white and black.
But black has other moves than checkmate. He could move his knight elsewhere and not checkmate white in one. The idea was to create a position for which the only legal move was checkmate whether white or black to move.