Here are some pictures.
This picture below shows something was applied on the cinder block, whether its from when the house was built 30 years ago or when they finished the basement I don't know. But some is flaking off. You can see efflorescence.
This picture is of the same section of the wall at a different angle. The underside of the carpet is stained near the bottom left of the picture where the bottom brick looks like it has fracture marks.
This last pictures shows the other section of the wall with carpet stains but not very much evidence of efflorescence. The top section of the brick has some dark stain. The 2x4 bottom plate above the brick looks clean and dry.
There are holes in the mortar in the first course of the bricks, I think it might be created by pests move in and out of the basement walls and using the wet insulation as their habitat.
What do I do to confirm if this wall is leaking?
We want to re-finish the wall again soon.