Thanks for the support.
1) only in case of primitives (pivot = bounding box center = geometrical
center).
2) I'm not sure what do you mean with "find a point a certain below", but you
can cast a ray and check out the '#isectPosition'
3) select the model, click on "Hierarchy / Affect Pivot Only" and set the
position & rotation of the pivot as you like.
cheers