Preserve tree structure when dividing curve

Not necessarily if (1) the planes are already perpendicular regardless of how they were made provided that you (2) did intend to orient those profiles perpendicularly at each plane.

I believe so - however because your plugins are installed already, grasshopper won’t warn you that you have non-standard components - it happens on a computer where such components aren’t installed. I suggest you check out the guidelines related to efficiently sharing the necessary items: