First, the Inverter is wired directly to the house batteries with the shortest possible cable length to reduce voltage drops and high current. As a result you can put the Use / Store Switch into the STORE mode but the Inverter will still have 12V power to it.
If you are on shore power, the built-in ATS will allow AC power to pass through the Inverter and your display will still be active (even if the remote panel is switched off). If you are unplugged from shore power, the ATS will switch over to the house batteries and attempt to provide power to critical items like a residental fridge of the remote panel power button is depressed (on).
If you want the Inverter to be truly "off" then you need to switch the Inverter power button off and remove shore power. Also, there is a built-in control panel on the Inverter itself and there is a remote panel inside the coach. The power button on the control panel built into the Inverter must be in the off position (button sticking out) in order for the remote panel to take control over the Inverter functions.
Now on to your next question...... if you have a residential fridge (120V compressor), then it should keep running if the Inverter is powered "on" and shore power is removed from the coach.
I am guessing the Inverter never powered your microwave from the factory..... unless someone rewired it. You need to download the schematics for your model to be sure which outlets should have powered when there is no shore power and the Inverter is switched on. Again, make sure the built-in control panel has the power button sticking out (off) and the remote panel has the power button depressed (on) when you remove shore power and test your outlets.
Now if those items truly worked when there was no shore power and you had the Inverter powered on with the original Inverter, then you need to look for loose wiring in a junction box or in one of the outlets that are daisy-chained together as part of the Inverter circuit. Perhaps you had some loose / bad wiring (common from the factory) and it shorted and took out your original inverter. Now you are seeing a couple outlets without power as a result of that bad wiring???
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