It's a VERY MINOR dampness problem. That is why he recommended parging the inside. He said it would be more effective than Drylok, etc., because it's thicker. He said they have a mix they use with fibers in it. Likely, I don't really need to do *anything* to the inside of the wall before finishing it. I'm going to use materials that can't rot or feed mold, to finish the wall. Not wood, not regular drywall. I do know why it's damp there. Many years ago, there was a gutter in that area that leaked a lot. Fixed about 10 years ago, but it probably wore away some of the tar that was painted on the outside of the wall. Yes, I could spend a lot of money to get someone to dig down around that wall, put a membrane on the outside. But as he said, and this seems sensible to me, try the easy, inexpensive thing first. If it really doesn't work - and it probably wouldn't cause me any problems if it doesn't, THEN I can hire someone to do the expensive thing.

Is the black "membrane" painted or troweled onto the wall or is it a flexible sheet that is adhered to the wall? IMHO the best kind is a cold spray=on modified bitumen (rubberized-asphalt) that fills any irregularities in the surface. Look at Tremco's Permaquick systems to seal the concrete from water penetration.

It appears you are concerned about the structural capacity of the foundation rather than waterproofing but I'll take up both. Waterproofing - To waterproof porous CMU ("concrete masonry unit" is the generic construction industry term — "cinder block" is light-weight CMU made with fly ash) requires an elastomeric (flexible) membrane like spray-applied modified (rubberized) asphalt applied to the outside of the wall and protected with a rigid fiberglass or polystyrene board. A footing drain completes the waterproofing system. Tar is not flexible and is considered dampproofing rather than waterproofing. I didn't know it was still sold. CMU construction - It is common to reinforce CMU with horizontal metal "ladders" in the joints. When the unbalanced fill (distance between the slab and the exterior grade) is greater than 3 ft, vertical rebars are placed in some of the CMU cores and the cores are filled with grout (not mortar of concrete). A mason might know if there is way to find them, Cracks - A vertical crack may be from exterior soil pressure especially if water is allowed to drain against it or a car parked there but a diagonal crack indicates a footing that has settled which often occurs at a corner. I can't say if the repair is a good one without more information or a photograph. You will eventually need to get a good mason to look at it so you might as well go ahead and call one.

My guess is the wood I-joists were damaged by water to the point where supplemental support was required to keep the joists from totally failing. It makes me wonder what is behind the waterproofing and what the brown is on top of the waterproofing. Then again it could be there just to take some of the bounce out of the floor.