Hello,
I'm in need to copy all data of arrangement of any items on the desktop and all visual settings from 'desktop behavior' menu. I just want to backup them for some experiments and maybe to move to another computer. Is it possible to copy adequate files?

Most of the configuration files reside in ~/.config. The absolute minimum for layouts and widgets are ~/.config/plasmashellrc and ~/.config/plasma-org.kde.plasma.desktop-appletsrc.