Guys, I have found solution eventually! :) :) :)

In main menu,

in "Extras-->K2-->K2 Categories" there are 4 categories by default.
I have added my 5'th own category in that menu.
In "Basic Options" I selected my own Category.
And in "Module Assignment for this Menu Item" I selected my modules, display: yes.
Now my items are displayed as sample items. Everything is OK.

Hope this will be helpful!

A-Design, Ashgabat city. ;)