Can't answer your solar questions (at least 1, and 2), but:
3. Depends on how you connect your solar setup. If the solar controller/charger is connected directly to the battery the store/use switch will do nothing.
4. When plugged into the wall the converter is providing 12V and thus everything will operate regardless of the position of the store/use switch (also note that the Microwave is 110V and not on the 12V system).
In general if your RV is plugged in you should have the switch in Use mode to maintain the charge on the batteries. When in Store the converter will be disconnected from the batteries and won't be able to charge. The only real time you need to be in Store mode is when the RV is in storage not plugged into 110V (in which case your solar setup should be maintaining the batteries).
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