If you can set the solar at constant 13.x volts same as the converter's float then leave all on, but if the solar does some 14.x first then drops to 13.x, then turn it off and just use the converter.
I turn my solar off at home because I can't stop the controller from going to 14.X first.
I have my TV on a power bar with its own on/off switch because the TV "off" is standby still drawing amps. I have not had any trouble turning the inverter on with a TV load, but as with a gen you should turn the inverter on first, certainly with a big load. I turn the inverter on as soon as shore power is off and the inverter stays on till we get home again. I don't bother with the small draw leaving it on-- With solar the inverter draw is trivial.
I clean the panels fairly often. The worst is seagull poop--big splatters. Mostly it is morning dew on the dust which makes them sort of muddy all over. Depends where you are how bad they get. Helps to be spry to get up there. :)