Referenz point at the intersection of a plane and construction axis

[SCALEMODEL]

Move a cylinder to construction axis

I thought someone else would chime in with your other request of converting Axis into Sketch, but if you could convert that is essentially a 3d Sketch, request that I would like as well.

It is bit strange way to do it but creating a cylinder somewhere to snap it to axis and projecting the face to the construction plane works.

Same video as above post.