RE:1) You won't often see the battery "full", unless you are flat out attempting to make it full. I wouldn't worry about the battery too much, the car has a good routine for making sure it stays within a certain, optimal range.

RE:2) I don't think its so much that it's jerky at low speeds, more so that it is (more) noticeable at these speeds. I believe what you are feeling is one of two things. 1, the valves are closing on the engine in order to avoid consuming gas. 2, the regenerative braking is being deactivated and you are moving to traditional braking.

RE:3) Well I don't really have a decent response to this one, it's cold. You don't operate so well when you are cold either. No car does, no human does. It's just flat out COLD, on an otherwise warm planet.

RE:4) Don't warm up AT ALL. What a waste of gas! If the engine thinks its too cold to operate, it will adjust the rpms on its own; it will protect itself. If you are really worried about longevity or MPG/FE, get a block heater, that is the only decent solution in cold weather.

RE:5) Yeah that's a weird noise but normal.

RE:6) Is okay? That's very good MPG in comparison to the regular civic or accord. Much less in cold weather.

In general, if you are looking for higher mpg. May I suggest tarabell's article as a solid starting point.