Set up of the shunt can go a long way for accuracy. Also the way sone batteries work out their own soc can also be interesting.
Possibly the same reason as above. The inverter is often set to shut down on voltage. So those settings would need to be checked.
Depends what is the wattage it draws? Some air con fans are 200watts.
You have some pretty commonly asked questions. And we all start somewhere so ask away.
See this complation here.
This is because on the GX in system set up, the battery monitor is probably not set to the shunt.