Sorry, cant see the pics (webfilter). I see you are in Philly. Those basement walls often have what the locals call parging on them. Its a masonry coating that flakes off over time if you have water issues.
Of course I'm guessing here but when u ask if its plaster thats what I think of.
Your first step is to deal with water OUTSIDE. make sure the ground slopes away from the house, the gutters are not overflowing and downspouts extend away from the house by 6 feet. Doing those things will likely dry out the basement. Then the old parging can be scraped off and a mason can re-parge.
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