1. Abaqus automatically uses perfect plasticity after the last yield stress. So as mentioned, you just need the first line of your table.
2. You still see higher values, since, as I mentioned, it is mainly caused by the extraploation, not the averaging. A Quilt Plot just uses the extrapolated nodal values and averages them to one value for each face of each element. It is not solving your problem.
3. When extrapolation generates such differences, then it is a clear indication that your mesh is too coarse. You have high gradients within elements and this causes the large overshoot in the extrapolation. Refine the mesh and this effect will go down. And read again what I said about perfect plasticity.
You can also plot the discontinities (Result->Options) in the results or request variable SJP to get indicators for mesh convergence. It is the duty of the user to define a mesh that matches the expected result quality. Or use the help of the Adaptive Remeshing method in A/CAE.