I extracted a curve from a surface (with P in edit mode, then Alt+C in object mode). I then duplicated a cone along this curve but the duplicated objects are distorted and I can't orient them normal to the surface. How can I duplicate the cones without distortion and orient them normal to the surface ?
The issue is your curve has unapplied scale. Apply it with CtrlA> Scale and it will work fine (note that you will have to re-position your cone):