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