Hi @davide76, I don’t see the problem with the shape in your image and file - the control polygon is twisted, but topologically valid. It looks strange because the quads are highly non planar and being rendered as flat triangles.
The SubD keeps the twist, but smooths the surface out.
Sometimes to get a SubD of a certain shape you’ll need a make a control polygon that self intersects, and this isn’t a problem, just like the control polygon of a NURBS curve might be self intersecting even though the resulting curve isn’t.
About the SubDThickenCurves question - I’m not sure I follow - can you post the file?
Currently if curves intersect, but are not split at the intersection, no node will be created. This has been the case since the first version, and hasn’t changed in the last WIP.
I am changing it for the next release though, so that curves will get split at their crossings.