It is wired only, no batteries.
As far as multiple controllers, I only have the one, can't test 2 of them at once. On my PC right now, I have a Xbox Controller connected via bluetooth and this controller via USB and they are working like normal two controllers for co-op in Humans fall flat. The app for Xbox/PC really only looks like for programming one of them at once. You can rename your controller in the app, so maybe you plug one in, name it, program it, save profile, then unplug, plug the other one in, name it different, program it, save profile. Then plug both in and off you go? Not sure though.