the antenna does not draw very much power, so you really just need a trickle charger on it. I am thinking of upping the solar power to also allow for the recharge of the lighting. just the antenna door really simplifies things. You can make it as fancy as you want by adding a second power switch such as car door lock remote control for remote open close (but would want a time on that so it does not over ride the light switch)
With a 12v system you can pretty much do anything that you might have in a car. You could get a small 12V heater, 12V lighting (LED is most efficient) and anything else you can envision. Plus 12V solar power is inexpensive along with the 12V simply power regulator.
the antenna should be able to get most doors open, but not sure on what the max would be. I would try to keep the load light in order to not wear out the antenna. The antennas can be found used for much less. Most of the items could be picked up for scrap costs. Using an old car battery would be fine, as long as it was not completely flat. Most car batteries are replaced with just under 12V. 12.6V is fully charged (6 cell 2.1V each =12.6V car battery) under 12 is considered time to replace typically.
You could even put the heater on the same circuit as the lights so that when the door is closed the heater turns on, or a 12V heat lamp. I would up the battery and solar system of going with a heater. a trickle charger 5W panel will not do much to recharge if you draw that much power!