Regarding boxes - this is what I found after removing the trim plate. What specific solution would anyone recommend given this situation?
I'm not going to soft peddle this so brace yourself. You really do need to replace those badly rusted boxes. When a box is supplied through Armored Cable or metal raceway the boxes are part of the Equipment Grounding Conductor (EGC) of the receptacle. when the connections between the cable/raceway and the box is corroded the continuity of the EGC is lost and the receptacles become dangerous to use because the EGC sleeve of the receptacle is not longer connected to the Service Disconnecting Means (SDM) and there is no low impedance pathway for current leaking from an electric appliance which has a grounding pin on it's cord back to it's source in the utility transformer so as to cause the circuits Over Current Protective Device (OCPD) to open and safely de-energize that tool or appliance. That means that a fault could energize the normally non-current carrying parts on the exterior of the tool or appliance until a pathway back to the source occurs by some other pathway. If that pathway were to be through a member of your family they may suffer an electric shock injury or be electrocuted. It only takes 3/100dreths of an amp passing through your body to stop your heart. It takes even less with infants, toddlers, and the elderly. That accidental return pathway doesn't have to be a particularly good one to injure or kill!
One way to replace those boxes is to undue the cable connector and push it back out of the box and into the wall. Then you can pry the box loose or, since it is a gangable sectional box, pry it apart with a large flat tipped screwdriver and remove the parts. Once you remove the parts prying the nails out of the bracket or the back of the box will be easier. Using a hardened pair of diagonal cutting pliers you can cut the nails near the end which goes into the stud and remove the now unfastened box from the wall.
With the rusted box gone you will have a couple of options depending on the conditions you discover inside the wall. Obviously you are able to get at the back of at least one of the boxes so any that are like that will be easier to rewire. To replace the boxes try an old work box in that opening and see if it will fit well enough to hold either with it's built in wall clamping wings or with Madison Straps.
The plastic box is only included to show another type of wing to hold the box in the wall. unless you go to the trouble of finding a plastic box with the internal bonding strap plastic boxes are not acceptable for use with Type AC Armored Cable. If only were Type MC cable there would not be an issue.
I f there is enough cable to reach the face of the siding consider replacing the flush box with a surface mounted weather proof box.
Any receptacle outlet that is expose to precipitation must be listed as weather resistant, those are marked WR on the receptacle face, AND have an In Use cover which is rain tight when a cord is plugged into it. There is no way out of both those requirements under the US NEC!
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Tom Horne