That's a lot of questions. 1st, you can do it but with 4,000 watts peak and maybe 3,500 continuous you will have to plan and test what the generator will handle. First thing is to try to figure the base load. This is what your AC to 12 volt converter needs to keep a few lights on, run the water pump, etc. Mostly the big load will be recharging the battery(s). After that consider TV use, running a micro, toaster or coffee maker. Using the generator to run an electric heater doesn't make sense if you LP gas heater works.
your generator will require you to ration power. Odds are you won't want to make coffee while you run the microwave. You may (will?) be surprised for a few times when you blow the generator fuse or kill it.
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