You can find the manual in the GOG client under Extras and, for some reason, Additional executables.
Yeah, it's weird which memories come back and which don't - I've figured out some things (or found them in the manual), but I still don't know how to select two or three members of a four-person squad. I can do just one, and I can do everyone (it's the little bar in the middle).
IIRC shoot is right-click, but you have to select a weapon first.
I tried re-playing the original Doom a while ago, and have no clue how I ever ran & strafed fluidly with the cursor keys and Alt.