that looks like the Navigation has no menu assigned to it – so WP automatically outputs all Top Level Pages in its place. I am not that experienced with Polylang but i believe you have to create a separate menu for the secondary language and assign that to the navigation as well.
Not sure what you mean “navigation has no menu asigned to it”.
There is a menu named “Main menu” and it was asigned as “Main menu in Greek”. Site is only in Greek yet.
By the way, not sure if anyone of you did something on the site, but the menu seems to be working properly now with the Polylang plugin activated. (I had left it deactivated).
I had deactivated everything related to caching.
Polylang had an update in the meantime though.
Maybe it was this, because I was trying to sort it out for a couple of hours before posting here.
It was realy strange because I am using GP with polylang in numerous sites and never had any problem.