The game saves each time you enter a room, but once you die : the run's over.
As for modding, it's just the usual bepinex, there's ton of documentation online about it, including on this thread.
As for not being able to walk, since it your earlier comment made it look like you're able to play the game, did you get the item that looks like an SM strap armor ? if yes : that item's bugged, avoid picking it up, if not : idk