Quoting: curt
1.) If I run the generator during the day for say an hour or so, will this help to charge the batteries for use during the evening and night (i.e. fireplace fan, TV)?
*** You need a battery charger. Power the battery charger with the generator. If it is necessary to run the generator because the batteries are too low for just the solar, or it's cloudy or whatever, run the generator first thing and let the solar fonish the charge later.
2.) Is there any switch required between the inputs to the inverter (solar panel and generator)
*** Solar PV charges the batteries via the charge controller and then an inverter sends 120 VAC to the cabin circuits. .... Generator charges batteries through the separate battery charger. No switches there. Batteries can still power the inverter; again no switches, etc. .... But if you want to directly power the AC circuits in the cabin with the generator you need a means to connect the generator safely to the cabin and by-pass the inverter. The simplest method is with an automatic transfer switch, next best is a manual transfer switch. That switches / transfers between inverter power and generator power.
3.) Suggestions on an economical inverter make and model?
*** Depends on how many watts you want / need, what devices you need / want to power.
4.) Can I use the non-inverter generator to feed the pure sine wave inverter to run electronics?
*** NO. Generators supply 120 VAC (240 VAC with some). Inverters run on DC input and produce 120 VAC output. (some 240 VAC). You can
not mix the generator AC output with the inverter AC output. It is either/or.