Keep it full for most efficient operation. As you empty it, add water bottles or something to it. I've found on my Snomaster that 36F is the optimum temperature to not freeze, and be quite cold.
A agree, lose the 12V cig plug. After you run your dedicated circuit you might use Anderson connectors. Also agree that pre-cooling before your trip will help a lot. You will not get 48 hours, but you might get overnight, this is going to depend on outside temperatures.
100W of solar would make a world of difference if you want to be somewhere for a couple of days and keep your battery topped up, of course a 2nd battery would also be nice with the right isolator setup.
A good test to convince yourself the 12v socket is not a good idea, is to let it run a while, then feel the plug, you will note it is very warm, if not hot. This represents loss of energy due to the design of the plug. Eventually it will melt and fail.
I agree you need a jump box for sure if you are not adding a battery right away. I'm adding a link to some pictures of my
fridge setup,
dual battery setup and my
power setup if it's helpful for ideas. There are also some electrical graphs the show how it is maintained on 100W solar power.