Well, I guess we're all getting a lesson in 'finishing the inspection' before we start 'groping for a solution.'

The original armored cable (BX) did not have a bonding strip. The jacket alone was considered a perfectly acceptable ground ... until the 60's came around, and some guys wanted to market a new product, one with a ground wire in it (MC). There was an endless debate, with each camp insisting that their product was better. The end result? Two different wiring methods adopted into the NEC - and the little strip added to the AC jacket.

Naturally, the sundry advocates didn't settle for that. As a result, many municipalities went on to ban AC .... while the NEC itself decreed that MC was not acceptble for health care facilities. Go figure.

The six foot limit Alan refers to is for flex and sealtite, where provided for flexibility. It was never applied to either AC or MC.

Getting back on point ....

Using the jacket for the ground path likely would comply with code ... so installing three prong devices is not an issue by itself. You still need to be sure there is a good connection to the box; too often the box isn't quite flush with the wall. GFCI (breakers or devices) might be a good idea, but I don't see the NEC as requiring them.

The clear acket on modern wire (THHN) is there only for ease of pulling. It, by itself, is not sunlight resistant. The underlying insulation is sunlight resistant, so i would not worry about those service conductors.
IF you are referring to a gray colored triplex on the PoCo side of the connections, then I would be concerned. There was a lot of bad wire sold to utilities, which now has it's insulation flaking off. Call them, and they'll replace it.

The calcification you refer to is certainly corrosion. I'd look into the cause. A loose connection will certainly encourage this, as will using a non-approved lug. It can also be caused by outside factors, like salt in the air.

I'd look at the feeder arrangement closer. If the PoCo is delivering 240 volts, there is no good reason to have only 120 at each panel. It is very possible that there was an illegal "service change," with the result that the PoCo upgrade didn't come until some time later - and the other hot wire isn't connected to anything.
(When permits are pulled, there's usually a line crew out there ASAP to upgrade).