Regarding the refrigerator: If you have access to shore power and can park on a level spot, leaving the refrigerator on is no problem. We park in a storage yard and have no power, so we can't leave it on. The day before a trip, we turn on refrigerator on propane to cool it before loading up. Just remember, when parked the refrigerator must be level. Failure to do so will cause permanent damage.
Check out Jensen for a radio that does all the things you want. If your dash opening is what they call two din units (about 4 inches high) there are several choices available.
