1) You need a generator
2) Sulfated batteries can be rejuvinated with EDTA. Deep cycle or RV batteries respond well to this treatment because they have thicker plates than standard car batteries.
EDTA RESTORES SULFATED BATTERIES
3) If you use a resistor to reduce power to a 12 volt
device you save nothing. The resistor burns electricity to reduce power. Touch the resistor, it will become warm when you run your fan.
4) Be cautious with any non vented fuel burning heater even a catalytic heater. Leave a window open for fresh air when it is on especially when sleeping.
"Coleman catalytic heaters are an ideal, and safe, method of heating a small cabin, tent or fish house when the temperatures drop uncomfortably low. Using a 16-ounce canister of propane in combination with the heater's built-in platinum catalyst provides cost-effective, flameless, long-lasting heat without fear of dangerous carbon monoxide buildup in the enclosure. For convenience, some models come equipped with an electronic ignition for flameless startup, and some also include a small fan (battery operated) for heat distribution. Note that regardless of manufacturer's specifications, it is always important to have a source of fresh incoming air, at least six square inches, anytime a heater of any type is used in an enclosed space."