Yep, turn off the inverter when not in use. Even at "idle" they suck power.
Yep, unplug the inverter when not in use if possible. Could be the inverter is not totally "marine grade" and may cause you to discharge electricity into the water.
Yep, do not have the inverter on when you start the engine. Likely, inverter is not ignition protected. If you have a battery switch (and you should), it should have ingnition protection built in. However, I'd play it safe (not tempt fate) and disconnect the inverter when starting the engine.
Sounds very much like WM took an off-the-shelf inverter, put their name on it, called it "for marine use" without changing or adding anything to it, and doubled (or more) the price. But, it should work fine as long as you take the necessary precautions.
J/36 "Zero Tolerance"