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.
I have no problems generating Intersection Curves in either 2D or 3D sketches.
In a 2D sketch the sketch plane is automatically the interection plane being used.
In a 3D sketch, it doesn't matter which element I select first. Or even if I preselect the elements before activating the Intersection Curve tool. The curve is generated without problems or lag.
Did you try doing a search on the forum for Horatio and Hamlet? (I had to do it before the post hit risier jumped in..., you kow the one, posts Did you search? to almost every question...)
Clown school isn't all it's cracked up to be, to much drama for my mama.