That would be a nice feature!
So, the child theme does not get automatically the settings of the parent, so I had to set the menus properly again. Now everything is ok.
Sorry for my noobiness 😉
yes,
you may see the differences in the two screenshots (links provided in my original post) of the website using the default theme and the child one. The header does not display while there are some unwanted differences in the menu items.
You may also find in my first post the layout of the custom menu used.
At the moment my site uses the expound default theme.
Thank you!