Hey Csaba,
regarding the second issue: it is difficult to give a definitive answer with the existing information – I will need to ask you for access to the admin back-end (you can send the details to support@satoristudio.net; I remember you’ve already done that once yet now the website doesn’t seem to load on my machine). I will also need more details about the problem: please clarify – as far as I understood you’ve created a copy of header.php with a new widget area code in the child folder, and added a new widget area in the functions.php file; and now the child theme’s header.php does not display the new widget area – is that correct?
Sincerely,
Andrii / Satori Studio