Tangents of one curve at division points

In Rhino i drawed three lines and put them in the grasshopper component curves. In the next step I divided these curves. My problem is, that the points aren’t on top of each other. I want the points like my reference picture. Now I have to find the tangents of one curves at the division points and use these tangents as the z-axis of a plane (plane normal). Next I have to solve the intersections between the planes and the other curves with points on. I am a Grasshopper beginnen and don’t know how to implement it. Can someone help?

Referenzobjekt.3dm.zip (12.9 MB)
Referenzobjekt.gh (10.5 KB)

Referenzobjekt edited v0.gh (16.0 KB)

almost the same as Quan Lis but with the normal planes and direction of the curves adjusted:
Re_Referenzobjekt.gh (20.0 KB)

Thank you guys!