1. The dash radio up until the 2012 models was run off the chassis battery, but if you're plugged in, it shouldn't matter much. You could run a wire from the coach batteries to the dash radio to use coach power instead.
2. To run sound from the TV through the speakers, you would have to have "audio out" on your TV, which I don't think the 2007's did.
PLEASE do not send questions via Private Message, my inbox fills up too quickly. Post questions in the forum as a new thread so that other users can benefit from the answers. Use Private Messages for sensitive information only (VIN, Contact info or things you do not want the public to see).