yes, that will be perfectly fine.

Yes, that is why it came on without ground connected. I see this on all of the cheaper cameras cause they dont isolate the ground in the internals, which they should. Usually see these cameras go bad within a year or so cause of it but when they are only $20 it isn't that big of a deal.

Backup camera works great, with the shape of my driveway and my Quickjack on the floor, it’s just way easier to back the car in the garage. So the camera is nice. It just has this annoying yellow banner “check surroundings before proceeding” that see nowhere how to shut it off and any other menus or touching the banner on the screen.