Is it possible to put the picked color to Artistic Color Selector so that proper hue, saturation and light pieces are shown?
(If not, is the problem that there might be multiple "pieces combinations" wich can be used to obtain certain colour?)

I tried to find answer to this in forums and manuals, but did not found.

Probably not. The artistic color selector really needs work done on it; the original author disappeared some years ago and since then we've only been able to do maintenance work on it, like porting to Qt5. It's not a complicated thing, though, and might be perfect for someone who wants to get started hacking on Krita...