Question
Do all points along a given path need to have increasing X-coordinates in a terminal? Can ROW handle a path line (e.g., pipeline) that, for example, heads towards a terminal, then heads backward towards the Central Site for a bit and then heads back towards the terminal again?

Generally speaking, all points along a given path should have increasing X-coordinates in a terminal. If a line does go backwards in reality, one can try to let ROW handle it approximately if the backward length is short. Some inaccuracy could result. If the backward length is considerably long, then special treatment must be given in order to obtain accurate results.