Hello,
You will need to have different headers for each language.
In order to have headers in different languages, follow the steps below:
1. Create a separate header in the language you need.
2. Take your default Header ID http://prntscr.com/lwox9s
3. Navigate to WPML Strings Translation and insert into the search http://prntscr.com/lwoyco
4. Press “translation” to open fields and insert header ID which you created for each language accordingly http://prntscr.com/lwozhh
As for the missing content. I see that products are missing. You need to make a translation of all the products and they would appear. Also make the translation of all the pages, synchronize menu.
Best Regards