Hi Andrii,
the copy of the original parent header.php without the widget area code breaks the layout. At this moment I removed the copy of the header.php from the child theme’s folder. I put it back today afternoon.
The main page works perfectly but seems like the sub-sites doesn’t work now, e.g: http://www.irodalmibableves.hu/tag-portfolio/bableves-es-csulok/
Regards, Csaba.