I dont have a greyhawk, but if it setup like my seneca in some aspects these might be your answers...
1) The radio can be powered by both the chassis battery OR the house battery. Meaning that the radio will not turn off unless you power it down using the power button on the radio or you turn both the ignition off and the main house off. My house power is on all the time while camping so I always just turn off the power using the power button on the radio itself.
2) My Seneca is not setup this way (I have a dedicated DVD player), however knowing a little bit about TV and what not I may have an idea here...on the back of your TV you prob have the input cables from the dash to the TV. Since it is black and white you most likely have a 5 RCA wire setup going from the dash to the tv but not all of them hooked up. Red and White is for audio, and then in the same bundle but more than likely together themselves is another red, blue and a green for the video. Those need to go into the corresponding colors on the TV. If the TV does not have that hookup, Jayco may have just used a composite input instead (yellow female RCA on back of TV). If it is plugged into a yellow one, you will only use one of the three video cables and it HAS to be the green one for it to work this way. Best option is to have them take a picture of the connections on the back of the TV and post it here. However another greyhawk owner could chime in before all this happens and just tell you what his/her setup is and you will be set.
2016 Seneca 37FS
DW+7 kids+2 dogs=bunkhouse required