Yes, you can use the main screen by itself.

You can load a DVD without removing the strap. It not possible for small kids.

Yes it does come with an AC Adapter

It uses the battery not the car so it doesn't matter if the car is on or not, DA.

No, it's only one dvd at a time

it hooks up to a lighter outlet only, all in car accessories do. surely you have an outlet that looks like a cigarette lighter somewhere in your vehicle, that is the outlet you use.

No, only the one screen holds the DVD. The other screen is only a screen. I suppose you could plug another DVD player into the second screen to watch 2 movies at once, but that just seems like a lot of equipment in the car! :)

Yes, I have a Yukon and the cords are plenty long enough.

One of the screens opens from the top to let you insert the disk. The screen is on a hinge and opens "forward".

As far as a 3rd screen, I don't think so. First of all, there is a "base" which can run indepentdant of the other screen. It holds the DVD and all the controls. The other screen is kinda like a receiver. There is only one outlet Audio/Video port to go to the receiver. Plus, I don't think they sell just the "receiver" screen.

As far as hooking video games to it, there is no inlet for the cabels on the base. On the receiver though, I am sure you could with the right adapter. It comes with a RedWhite Yellow adaptor, so if you plug that into your gaming system, then plug into the receiver screen AV input, i think it would work!
I hope that answers your question!