Plane stress is an approximation that assumes stress in the axial direction is zero. As you can see in the Axisymmetric solution, zero axial stress a poor assumption, especially as the thicknesss of the rings becomes larger, so axisymmetric is more accurate.
You can apply a displacement of X = Free, Y=0 to any one vertex. It doesn’t matter which one. The one point you pick is the point from which all the nodes will expand away from. You can only notice which one point was picked when you plot Deformation. If you plot stress, you can’t tell.