Hi Chouby,
Thank you for your quick reply! This version solves the problem and now I can save and see my menus.
But I have noticed two other things when playing with the menus.
I test adding a menu to a position in the template both from the menu edit page and from the Customize Theme screen.
1. From the menu edit page
As you can see from this screenshot:
https://www.dropbox.com/s/4i73o5g5vqywkej/main-menu-en.png
There's menu which is assigned both as top primary menu and secondary menu in English. But when I try to remove it from the secondary menu position and hit the Save menu button, when the page is reloaded, the check box, marked with red is selected again and the menu is still visible in the site. When I try the same with another menu for Bulgarian, it works. But when I remove the Bulgarian menu from the secondary menu position, the English menu is also removed from its secondary menu position and can not be added again, until the Bulgarian menu is re-assigned to its secondary position.
2. From the Customize Theme screen
When I try to remove the English menu from the secondary menu position in the Customize Theme screen it works and the menu is removed. But then when I open the English version of my site on the secondary menu position I see the menu, which is assigned to the Bulgarian language and is not supposed to be there.
When I remove the Bulgarian menu from its secondary menu position it works and in the English version of the site I see the English menu, as it should be.
Probably I miss something? Is it possible to have a menu on specific position only for the one language, but not for the other (its place to be empty)?
Thanks again and have a great day.