I use a combination Ctrl + R, to divide the surface into 2 parts. It appears pink line, but I somehow for some polygons can pave it only from the top down or from left to right only, and I need the opposite. What am i doing wrong?
In the screenshot the red outlined, I can not lay a pink line
Interruptions in Loop-cut means you need to inspect the geometry closer, often it points to faces not being joined by the edges that you think they're joined with. Some discontinuities are easy to overlook, but also easy to spot
Play close attention in Face selection mode to the locations of the dots that represent the median point of faces. If you see a dot on an edge that's a sign that you have accidentally created degenerate geometry, or if not degenerate then possibly unintended.
A side ways zoomed in view of your screenshot.
Selecting all in Edit Mode and Remove doubles can be used in most cases, except when you intentionally have vertices closer than the threshold that Remove Doubles operates on.
