Thanks everyone for the great answers, examples, and especially the safety info. Here are the updates, from following the advice:
took the microwave out of its cabinet, and plugged into outside power source. Has the same quirks, and I will now run it by a local repair shop that has very affordable estimates/diagnosis. Will have fixed or replace if needed. I will still test the outlet as well, just as a precaution.
Will check the 120 V refrigerator heat element. Have not had time yet, but watched a couple videos, and will check the manual over the weekend.
Will look for a replacement switch for the water heater.
Even though the replacement vent/fan is on order, I figured I would look into why the current fan was not operating, in case it gives me insight into the wiring condition. Now I see the answers, the fuse question on the fan was trivial, but I wasn't sure when I asked.
I'll get the sensors/alarms replaced as a priority. I will probably go with basic battery power models immediately, then make a decision on replacing flush mounted built-in models.
As soon as I have clear, dry weekend day free, I will launch a major campaign to check all caulking and sealing, and re-seal as needed. This will be a priority. The Dicor lap joint compound is coming in the mail soon.
Thanks again to everyone; I will probably look back on my questions in a year and think how simple and basic they were, but everyone has to start somewhere, and this is my initial starting point.
