I’m trying to do a ribbed detail on an assymetric bottle and I wanted to split it with pulled curves.
After pulling few of the top ones are warped downward a bit and I want them all to be straight and parallel. How to do that? Should I use different command? Or my sufrace should be fixed in some way?
The Pull tool pulls the curves onto the surface based on the surface’s normals at each point, see below. You could simply use Project in a planar view, and then Trim the curves with a curve extracted from an isocurve of the surface, see below. Then you can use those curves to Trim or Split your bottle surface.
That aside, your surface is immensely complex for what is essentially just a "puffed up and squashed cylinder. It is also not centered, which is not ideal; see the four bunched-up CVs at the “almost” centre. Normally, you’d just build one half and then mirror-copy afterwards.
First, I’d build the bottle shape properly centered, and also much simpler; you can build the primary domain as a very simple single span degree5 surface, then mirror-copy later. The simpler the surface, the simpler the projected trim-curves, and the simpler whatever you intend to do with the ribs.