In order to translate the Header, it is necessary to create separate headers for each language. The Header is translated into Strings Translation by ID. Header ID is taken in the Header page as shown:
The next step is to find the proper string by ID: navigate to the Strings Translation and insert into the search:
Finally, press "Translation" to open fields and insert header IDs which you created for each language accordingly:
In order to translate a custom header, it is necessary to create a separate header each language and set them in the Custom Header drop-down of the Page options
All the menus should be synchronized in both: translating the default header and any custom header.