Hope I can help a little.
First thing- I would strongly recommend going to SDC on the Weds or Thurs evening if at all possible. At the very least DO NOT GO ON SATURDAY!! The crowds are enormous on the weekends, so go on a weekday if there is any way possible to do it.
There will be eating places open throughout the park throughout the whole night. There are some that will close a bit early (in particular the buffets close a couple of hours before park closing as I recall), but there are still plenty of options for food. Most of the walkups stay open til closing time, with a few staying open a bit later (e.g. funnelcakes), and that's true of a lot of the other eateries as well.
As long as temperatures don't get to cold, all of the rides will continue to run. Generally the only time you're going to have to worry is if it's getting close to freezing, which it can do that time of year. But as long as it's in the 40's or above you won't have any problems. There won't, of course, be any water rides open.
Temperatures can vary. It can push near 60 for a high sometimes, and also get down close to 0, so be prepared for anything. Generally though you should be ready for a high in the upper 40's to 50 and lows in the 30's somewhere. Be sure to watch the weather forcast though, and even then be prepared for anything. We had one time that they swore it would only get cold on us and it dropped 3 inches of snow while I was working on the train.
I haven't been to much of the Branson Christmas stuff, as I was usually working, and when I wasn't I live the other direction. The Shepherd of the Hills lights are pretty neat though- it's a one hour drive through with hot chocolate at the end that can be a lot of fun if you're into that. The "Branson Gift of Lights" actually costs more money and is a shorter drive. And lots of great Christmas shows throughout town, but I'm honestly not even sure what is free.
Not familiar with the cabins offhand either, but they are listed on hotels.com and I've found their reviews to be a pretty good indicator overall, and it gets good marks there (4.5 out of 5- the only negative I saw being someone who apparently didn't realize that ants live in the woods. lol)