We cool ours down using AC the day before travelling. I usually add frozen water bottles to help it along as it takes several hours to cool down, and don't load food until a couple of hours before we are leaving. Ours will automatically switch to propane (if tank valves are open) when we unplug the AC power just before we start travelling. Hope this helps.
Yes, and Yes. Not dumb at all. It's good to run your reefer a good 12-24 hours before leaving and running it on propane or 12v when in transit is perfectly fine. The only precaution is to turn it off during fuel stops. (Although.. the number of people that do and don't is probably 50/50.)