Ok will pass that on -

What about the crack in the concrete and the bitumen paint?

Unless it's a gaping crack, I'd say that's normal ground movement. The bitumen was probably added to try and remediate the leak but it's never going to work. Water will always find the point of least resistance so you have to make gravity work for you by creating the least resistance below the slab.

Been through this myself recently but it was a more difficult sloping site with a basement retaining wall. Had to bite the bullet and re-dig the drain in the basement. Couple of huge weather bombs since then and not a speck of water getting in despite sub-surface rivers of water running through the clay under the house.