Factory head unit
Factory nav system. Not sure about "factory tv system". I can watch DVD's on the screen if that answers your question. The feed comes from the DVD players and monitors in the head rests.

The camera is mounted on the tail gate right next to the license plate (I'll get a photo).

Yes, I have something with a video input that I could use the test the feed, just need to know where to access the connections. I have a multimeter.

I did notice over the weekend when I was looking at it that there is a small drop of water in the lens - on the inside of the clear dome. Not sure if this is just condensation or somehow water go into it when I was washing the vehicle.