Well this is just experienced opinion and you should consider everyone's experience and routine is somewhat different because what they do is different. For me I boondock for college football tailgating and an occasional fair/festival weekend. Other than that I have generally have full hookups. So based on my experience some generic answers to your questions
- Generally it is recommended you equalize batteries monthly unless you take charge below 30% SOC then equalize immediately
- Your solar panel is just slightly larger than should be used without a controller with 4 6v batteries. Get a good quality controller (I like morningstar) and you can leave the solar system on all the time (Mine is never disconnected)
- Generally you shouldn't take batteries below 50% SOC (12.2volts resting or around 12 volts with a small running draw) but 6volts are pretty tough and can be taken down to 30% SOC occassional (maybe 11.5 volts running)
- Many good quality MSW inverters work fine but it is really dependant on the equipment not the inverter. I use PSW and don't worry about it
There are many good on-line sources to learn from. Goggle and time is your friend.