After some funny moment about 3D sketch and assemblies, I just discover another funny sketch : the intersection curve.
If I define a surface, and then a plane, the intersection feature is laughing like a drain so much that the program forgets to build anything.
If I define the plane BEFORE the surface, then Horatio is coming on the stage, and spout with a deep voice : "That was the question, Hamlet, that was the question".
And the intersection curve appears, like by magic.
Moral : before using SW, have a training course of clown.
Amidst your bad corollaries, I can't understand what your issue is.
As a side note, I seem to be pretty successful at using intersection curve. I have yet to attend clown school; that may have to wait until a mid-life crisis.