How can I repair the degraded surface of a concrete slab and wall?
Vinyl cement patch is what you're probably after. It's designed to bond well and handle impacts and movement in thin applications much better than concrete or mortar. It can be feathered to a thin edge. 

Mix per the instructions on the package and apply with a wide putty knife or trowel. 

Be aware that you won't have good results spanning from one concrete object to another. There's almost certainly seasonal movement between the two that will tear the patch apart. Use a control joint where necessary.