Recoil turns a shooter mechanic into a movement system: firing pushes you backwards, so the way to get anywhere is to shoot in the opposite direction.
It's a genuinely clever idea, because aiming becomes navigation. Every shot is simultaneously an attack and a jump, and the two intentions frequently conflict.
Firing pushes you in the opposite direction, so aiming down launches you up and aiming behind pushes you forward. Shooting is your only means of movement.
Usually yes, which is what makes each shot a route-planning decision rather than a free jump.
Yes — a light 2D game with nothing to install.