The snap to curve will work and the two object don't have to be combined, what you are most likely doing wrong is when selecting the move tool you are probably selecting an axis instead of the center and free movement.
Still wouldn't mind figuring out how to snap/create a vertex where two edges intersect though.
That's exactly what I do for that part but I still can't snap a vertex to where two edges intersect and according to my instructor today it's not possible. No idea.
This is not the best way to get two objects on top of each other though, the easier way would be to move the top objects pivot point to the bottom (hit insert key select y axis on pivot and hold v key and MMB drag over bottom vertex of the top object and then hit insert key to complete or less accurate but quicker hold down d and manually position pivot) then in object mode select the top object and hold v key and MMB drag to a top vertex on the bottom object.