Yes, that plate with a coax outlet and a 12vdc "cigarette lighter" outlet is your television connection. Connect the coax to the TV via cable. There should be a small button on that plate, which will make an even smaller LED light up. That is an amplifier that must be on for your antenna to work. The 12vdc plug is available to you if you have a 12VDC TV. (I do, it's great for boondocking - everything works even when not hooked to shore power). BTW, that 12vdc outlet is fused to only about 7 amps, so don't think about using it for anything with a heavy draw.
The water assumption is correct, and even more so. When you have city water pressure applied to the TT, all cold water, including the hot water heater inlet, is fed by city water. You didn't use your fresh water tank on this trip. When city water is applied, you don't turn on your water pump. All cold comes from the city. When you ARE NOT connected to city water, then turn on your pump, and you will draw from your fresh water tank. We always keep about 1/3 fresh tank to be able to use the toilet and sink while on the road, even when we know we're going to a campsite with hookups.
Marty and Martha
2015 Z-1 211RD
2012 Nissan Titan