The created two cylinders are separate objects (despite they have the same color, that’s quite lame), you can use the boolean tools to fuse/subtract them.
I see what you expect from the first screenshot. That circle should not even appear, because in the current concept you can sketch on faces. The curves you sketch on faces should be trimmed by the faces boundaries. The first case could be solved simply with snapping (to the center of rounded faces), without constraints.
I am not sure what you mean by construction plane, would you like to move the grid to that plane? Because that will be included in the next release with the orthogonal views.