How to properly top a parapet wall with coping stones?

Question

I have a flat-roofed extension with a parapet wall (built by previous home owner). The parapet is topped with once weathered concrete coping. The extension is about 15 years old and – I think – the walls are a single layer of cinder block. (Due to being 9" thick).

During protracted rainfall I get pretty bad water ingress into the interior ceiling and walls below. I'm fairly sure the flat roof itself is fine. It's always the edges, and particularly the corners.

The coping stones are very weathered indeed, with almost no sign of their original, smooth grey surface. I went out to repoint them and coat in some waterproofing, but in the process I noticed a loose slab, so I had a peek underneath.

I notice the damp proof membrane doesn't quite span the width of the wall and is barely bonded at all to the surface beneath.

Firstly, does this seem like a likely cause of water ingress?

Secondly, has this been built badly?

I'm inclined to get my builder to do the work of completely replacing all the coping, but I want to know exactly how it should be done, and what materials should be used, so I can oversee the project.

Specifically:

Should the DPC go to the edge? or even over-hang the top of the block work?
My local builders merchant sells DPC rolls at 225mm width, which seems exactly the size of a block. That doesn't account for the extra thickness of the render on one side, nor the roofing felt on the other. Should I get wider?
How should the DPC be bonded to the top of the block-work? You can see from my photos that the surface under there is in a bad way.
What mortar mix would you recommend? The existing mortar is very yellow, which I'm guessing may mean heavy on soft sand.

Here are some photos: