The distributed toggle and the core setting in the Home/Solve section is for the solver and not for the mesher. If you are using the default mesh method (sweep/patch conforming tetra), these methods are not parallel. However, if you have multiple parts in the model, each part gets meshed in a separate CPU. If you have a multibody part(for conformal meshing), then the bodies in the multibody part are meshed in 1 cpu.
For information on memory requirements, check the Mechanical APDL documentation on performance. You can see information on how much memory is needed for 1 Million degree of freedom for sparse solver, iterative solver etc
Chapter 4: Memory Usage and Performance (ansys.com)
If you use Multizone method, this method can use multiple CPU's .
Without looking at the model, I am not sure what could cause the meshing to be slow. For meshing, you have two setso of input that can check - mesh controls(sizing, method, details of mesh) and geometry. If this is machine related: Is this a shared resource that you are using? Are there other process running on this machine?