1. It is usual that a fence is replaced with the posts & rails on the same side as they were originally unless the neighbours agree otherwise. This is so even if just one party is paying for the fence. But that's just a convention not a law.
2. Good practice would be that the surface and any areas exposed to replace a fence should be returned to the original condition (or better). That means that all those cement surfaces should be renewed and level.
Have chat with the neighbour and then the contractor. If you have already paid then you might have a fight on your hands. If not then don't pay (or at least withhold some) until the job is done properly.