Raphael Assenat's webpage on the Sega Saturn joystick confirms that the Genesis Multi-tap, Saturn 3D controller and the Saturn mouse all use the same protocol.
I couldn't find any specifics on the Saturn mouse though.
1) Have you tried making the adapter to connect the Genesis joypad to the Saturn console? It's said that the Saturn supports this natively.
The adapter is probably wired like this:
Saturn Genesis pad
pin-1 pin-5
pin-2 pin-2
pin-3 pin-1
pin-4 pin-7
pin-5 pin-9
pin-6...