1 - Yes it is possible, the mouse and keyboard does it, but might take a bit of software on the PC side;
2 - PS2 uses 3 wires, basically (DATA, CLOCK, GND), with a 4th wire for powering the device itself, which you don't need with an external power supply;
3 - a keyboard/mouse is usually reset at pc startup, you need to implement this in you design (if I'm not mistaking there is a command that is sent to the device on the PS2 bus);
4 - google is you friend, you can find the vhdl code for PS2 very easy, also the protocol description is out there.