Make it possible to edit on a plane such that clicking in an empty space adds a point on that plane in that position and points on that plane can be dragged within that plane.  Also, clicking a point not in the plane shifts the plane to the parallel plane intersecting with that point.

Also a button will be used for toggling editing within the normal 3d space or a specific plane.

There are a number of options for how to represent an editing plane graphically.  The most attractive options would be minimal, yet provide sufficiently clear visual information.

I suggest creating a crosshaired outlined box in the plane around the center axis.  Shifting the plane to another point will actually center the image on that point.