Repair front stoop

I've got a front stoop in need of attention. Basic construction is concrete block external walls with soil/sand filler. Steps and some trim edges are red brick.

The top edges are brick with the center being cement with blue slate pads. This is where the problem exists as moisture got underneath and has pushed up the slate to where they might cause a person to trip. Much of the surrounding cement is weak and crumbles.

I know the basics will be to remove the slate and chisel out the old cement. Question is then how to best prepare that project so the new cement will hold properly? Do I need some kind of chemical prepping so the new will adhere to the old? How many inches thick should that top layer be for strength and durability?

TIA

This old "cement" is probably actually mortar, not concrete???

("Cement" is the dry powder that is used to make concrete, not the finished product, just for terminology so all talk the same thing, btw)

Anyway, what you need depends on what you find. If it's just poured on the fill, need to ensure it's a good base and, if it were me, I'd pour a standard 3" sidewalk thickness as the base and then re-lay the slate in a mortar bed on that rather than put it in the concrete itself.

If what you're talking about is actually a mortar bet to begin with, where to go after getting it off depends on what you find underneath--it may be there's a decent subbase and a new mortar bed will be good for years, maybe it needs replacing, maybe...