(1) Yes, the Amiga mouse port supplies +5V for joysticks, etc. Maybe an adapto will connect to it, maybe not.
(2) Never seen one, but there might be something out there.
(3) The PS2/DB9 adaptor to which you refer may be a serial adaptor, meant to plug into a PC serial port with applicable software. It would need special software on the Amiga side. There might be something on Aminet.
(4) You forgot to turn on the power.
USB devices deliver data in bursts or packets. Amiga mice deliver data as contact interruptions. I don't know what is inside those adaptors, but they had better be pretty clever.
With all the money you spend on adaptors, would it not be cheaper to buy a USB card for your Amiga? Like the Highway, Subway, Norway or Thylacine? At least then you would get full support.
tony