Also, is there a technical possibility for playing on the same PC without a split-screen mode, making turns on controlling the custom characters?
Well is always possibility for that. Just switch who controls who. Not sure what functionality could be added beyond you and your coop partner switching places.
I would assume keyboard and pad should work as speperate controllers. As far as I know that’s usually how it’s done. In split screen coop UI each of you gets separate screed so UI should be able to adjust, though I don’t know how well K&M UI would adjust to having just half of the screen to work with.