Hi Mala,

re:
> No points to pick...I do not understand such things. Sometimes you may
> see the points of surfaces or objects, sometimes not...

You can always see surface control points for an individual surface not joined to any other surface. You can use Edit > Separate to break joined surfaces apart into individual ones.

For an object made up of several surfaces joined together, you can only turn on control points for those if all the joined edges are natural edges of the "underlying surface" and they have the same control points at that natural edge. If the control points for the "underlying surfaces" are different then control points will not turn on because it is too easy for the surfaces to be pulled apart so they are not intersecting anymore at what is supposed to be a joined common edge.

There is some more description of this and some example images at:
http://moi3d.com/FAQ#Q:_Why_does_show_points_work_for_some_objects_but_not_others.3F

- Michael