You have an issue, plain and simple. And like nestor said, how much remains to be seen. If you are able to remove the sheetrock were it is damaged, most likely there is much worse happening on the back side.
Sheetrock does not belong in a basement with stone walls, you need to remove the connection of the walls and let some air in there to let it dry out. A dehumidifier and a flashlight are all you need to monitor it. take the flashlight and put it against the wall so you can see all the bumps and fuzzy stuff growing on the wall...that is the mold.
Folks need to realize, OLD basements are for cold storage and storing non cellulose based stuff. New basements can be finished into rooms, only if the water and "moisture" in the form of vapor or condensation is treated from the exterior only. Those painted walls you have are nice to look at, but do not create a good solution to your problem.
A real professional did not finish this basement. It looks to be done by an inexperienced carpenter or the homeowner.
My opinion is just that, an opinion. But from my experience, this is just a problem waiting to get worse.
Hope this helps.