port that supports 4 screens?

With DoomLegacy you could start 4 copies of the game in Window mode and have all the windows on the screen at one time.
In Linux you just open 4 console windows and have each one join a net game.
I have never tried this ...

The real problem is the controls.

Open the Doomsday console and enter the following:

makelocp 1;makelocp 2;makelocp 3;viewgrid 2 2

Now configure the controls for the other three players :) (Which admittedly has to be done manually via the console)

Yes, thats correct. If you get stuck, consult the wiki for detailed info on control/event binding.

Just bear in mind that splitscreen is still WIP in Doomsday (theres no GUI for a start), so you'll probably encounter the odd glitch.