1) The 12v is in a wall plate with what looks like a coaxial cable screwed/plugged onto the top half. If that cable is the TV booster, then yes, it's on the same plate (someday I'll figure out what a TV booster is).
I will try to explain the TV antenna booster because if you don't use it properly you may not get cable or over the air TV reception. Many times I have been frustrated with the TV reception only to discover that I did not have the booster properly turned on or off.
There are three coax connections on the back of the wall plate, one from the roof antenna, one from the cable input connection on the outside of the RV, one to the rear TV. The coax connection on the front of the wall plate goes to the front TV. When you are using the roof antenna, you have to turn the booster on by pressing the button on the wall plate so that the LED light is on. If you are using cable at an RV park attached to the outside connection on the RV, you have to turn the booster off by pressing the button so that the LED light is off.
The booster uses 12v and the power outlet is added as a bonus, it is also is a signal splitter and multi-input source switch - does a lot for a little wall plate.
Bob