Hello.

Is there any way to make a full designed frontend edit form page in K2? I made it to open in a new window but it's just a form page without site header, footer and the other site elements. I really need to make the frontend edit page looks like just another site page.

You can override the itemform.php file of K2 and the component.php to change the look & feel of the form.
More on overriding can be found here: getk2.org/documentation/tutorials/174-templating-with-k2-and-the-concepts-of-sub-templates

I know about overriding and use it often. K2 displays editform page without site header, footer, sidebars and the other elements in index.php. It's just naked form page. How can I change it?

When you see ?tmpl=component in (any extension's) URL then the component.php file is being used instead of the regular index.php.
This applies to all extensions.

To understand what component.php does you need to read this post.
docs.joomla.org/Understanding_Joomla!_templates

If you need to isolate K2 in the component.php so it does not affect other extension you can include these modules (header/ footer) only when K2 is being used.

An example would be: github.com/kricore/Advanced-templating-with-K2/blob/master/_inc/cheatsheet.php#L26-L44

Thanks! I found thisin the edit function of item controller. So I just changed it toand got exactly what I need. Solved.