Hi,
so far I have managed to get this approximate result manually and via a slider. How exactly can I achieve my goal?
Thanks in advance to all of you!
Mario
given a Starting Point, Pull point will give you the closest point to Starting Point on a Geometry: there’s no equal distance involved (if I have understood the problem correctly)
given a Point, I’d suggest to go with Spheres to find intersection points on next curves
for instance, given P, on the first Curve, you can find P’ and P’’ on the second Curve, and then P’a, P’b and P’'a on the third Curve, this is just a sketch to show the concept
equally distanced points on different curves.gh (12.6 KB)
please consider sharing your GH files together with screenshots, files do make the difference 
3. Attach minimal versions of all the relevant files
equal-distance-between-points.zip (46.6 KB)
Here is the files, sorry for neglect.
In the meantime I will study Inno’s solution (thanks so much Inno!)
I love your solution, inno! Great job! But what if I wanted the closest possible points between the curves?
OK, all in all this solution suits me. Thanks again!
in that case you won’t need to create spheres to force equal distance, but Pull Point would be enough