How would you write this up?

I have writers block its too late. How would you write this up?

Simply state the issues you observe… improper grade around the concrete slab as well as downspouts not properly draining away from home resulting in erosion around (name the area). Recommend that a professional landscaping contractor correct same which includes pushing gravel back under the slab (poor job on the slab by the way however based upon my experience I don’t foresee it failing). The downspout should be cut and the elbow repositioned and/or install drain pipe extensions on same.

Was the concrete slab recently poured?.. wondering if they were using bricks and other objects as a filler

I would also recommend that those type of thresholds be properly caulked underneath and properly supported…if not they end up separating from the brick moulding which will eventually deteriorate. Also check to see if they actually caulked between the brick mould and threshold…most of the time the installers mistake adhesive for caulking.

what is that sticking in the concrete?

Slab undermined. Repair, as needed, to prevent damage.

In the upper right of the 2nd photo? Looks like a bit of brick veneer… supported on a brick ledge or properly attached angle iron, I hope.

Looks like it could be expansive soil. If it is the sidewalk should not be attachend to the structure.