I setup k2 comments only for registered users and comments counter(anchor) shows also only for registered users. But I need shows counter(anchor) for everyone.

Hello,

In your overrides, locate this line:
github.com/getk2/k2/blob/master/components/com_k2/templates/default/category_item.php#L252

and remove this part:
&& ( ($this->item->params->get('comments') == '2' && !$this->user->guest)