Yes the first element has correctly been updated to reflect that we travelled a distance d.

No the ray should be {0.01, d} since the second entry will tell us that we moved a distance d.

No the ray should be {0.01, 0}, the first element is only the height above the optical axis which doesnt change as we have a ray initially travelling parallel to the optical axis (which is why the second element is 0 and stays zero.

No the ray should be {0.01-d, 0} as we get closer to the axis while travelling a distance d, since the second entry being zero means we are travelling downwards.