1. From what I understand, ALL outside kitchens have AC powered refrigerators. Your's is not an exception. You should have caught this before you purchased it.
2. Don't know of any RV that connects the entertainment center to anything but the television located AT the entertainment center. The only lead going to other television locations is the coax cable for over-the-air television. Unless you have one custom made, every RV is factory made this way. Again, you should have asked about this before your purchase.
3. The outside inputs are for:
Satellite: All satellite systems require a dedicated line going to the satellite receiver. They do not work at all if they are connected to the campers television booster or electronics. That line (only a single line) will run to the entertainment center where you can attach the satellite receiver.
TV/Cable: One is usually designated as an "input" for connecting to a cable system, maybe provided by the campground. That cable signal will feed to the coax jacks inside the trailer wherever you have a coax jack to hook up to the television. It sounds like you also have 2 additional jacks on the outside of your camper for convenience. Here again, they are connected to the same wire as that will use the campground cable.
Also, that same Coax wire for the campground cable is also used for over-the-air. Turn the television booster off (that little green light with the black button), and all of your jacks will work with your over-the-air antenna on the roof of your RV. Everything except the satellite input jack. Remember, it's dedicated a dedicated line, not connected to the camper antenna system.
So, if you use your television antenna, turn on the tv booster and the little green light will come on. The antenna can be used on all the jack, both inside and outside the camper. So you can position a television almost anywhere, inside or outside.
Turn the booster off and plug in a Coax line to the campground cable and all the jacks will be cable ready. Scan with your individual television, or get the necessary box from the campground and you'll be able to use the box on only 1 television.
Hope this helps explain the jacks.
By the way, I've never heard anything but 120 volt AC refrigerators in the outside kitchens.