Mark, first off congratulations on your purchase of an oliver, one of the finest rv's made. I'll try to answer some of your questions. On the charging, yes to all of the above,your converter/charger takes over, and when your solar is insufficient you either need ac current from a plug in or generator. On the consumption side, all of your d.c. appliances draw from your batteries when in use, the solar just replenishes the power used and the converter/charger takes over power management when you're plugged in either with shore power or generator.
Try not to go below 12.3 volts when your batteries are at rest, that's the 50% level with agm batteries. When the solar is charging the voltage can go as high as 14% but you have to wait until the batteries are at rest to get a true state of charge with the solar controller we have.
geO is correct about the battery monitor, however I've done without so far by just monitoring my voltage early in the morning before the sun comes up and starts charging my batteries. It takes a while to figure your usage out without a separate monitor.
This method is crude at best but so far so good, you shouldn't need to monitor your batteries when plugged in your converter takes over that task.
I would strongly advise doing some research on battery management and inverter usage, there are multiple posts on this subject throughout this forum.
Steve