@greentoaster said:
having the center of the cylinder coaxial with the green or red axis seems impossible.
For all these problems, drag out a rectangle near, but not touching, your work. Push/pull up to box size. Triple-click, group. Place the thing you want on the appropriate face. Hold the shift key down to lock orientation. Go do your thing. (Works for Circles, Polygons, Rotate tool, Protractor, ...