Liftagte: Is this a power liftgate? Is the liftgate closing/dropping on peoples heads when they are under it or is it just not opening all the way and people are bumping their head into it? I believe the opening height is adjustable, maybe try resetting it. I don't have a power liftgate on mine, but I noticed the max height is not conducive to taller folks as I have to duck to make sure I don't hit my head on it.
Battery: Have you gotten the "christmas tree of lights" on your dash from the low battery? Any other issues/warning lights on the dash from the low battery? Other posts here seem to indicate that low batteries can cause a multitude of other problems to potentially appear.
Auto lights: As far as auto lights, they are all programmed differently from vehicle to vehicle. Are yours consistent in that they turn on/off at the same darkness/brightness levels each day or do they turn on/off inconsistently (at different times each day)? If they are consistent, just not turning on/off when you would like, there may not be much you can do as I don't think the programming can be changed (maybe you could replace the sensor and see if that changes anything, or you could obscure your existing sensor so they turn on sooner and stay on longer). If they are inconsistent, perhaps it is a bad sensor or wiring issue. Most of the vehicles I have currently have with auto light sensors also have DRLs, so I don't really worry about exactly when the sensor turns the rest of the lights on/off and I don't pay attention to the differences from vehicle to vehicle.