Regrettably I can't answer all your questions, Dan, except that you should have solar input even with your Master Switches off. My coach sits by my house that way and my Magnum inverter panel shows batteries at 13.2 volts except on the very dark, stormiest days. I rarely have occasion to plug into my 30amp RV outlet because of that, and my bats are original factory ones, 8 years old.
I am surprised you found fuses in your electric bay, since presumably there should be one on or near the solar controller; even BCS couldn't find that one for me when I asked a few years ago. Just about everything in the electric bay is on circuit breakers, not fuses, and no solar ones are on my bay's legend.
There should at a small green lamp glowing on the controller's visible circuit board if all is well. I presume nothing has befallen the roof wires and the panel isn't obstructed, covered, or radically dirty in any way. I guess I'd check for that elusive but fabled fuse on the controller circuit board or perhaps inline nearby; yours may be more obvious than mine. And check that wires large and small, positive and ground are all cleanly mounted to your battery posts.
Joel