Hello,
To set up top header section on the right as in the screenshot, please go to your Admin Dashboard > Appearance > Customize > Menus.

Then create two menus: one your Desired menu and add Items in the desired menu as per your requirement.
Next is Social Menu and add custom social links as per your requirement.
Please refer to below link for the detail info.

http://image.prntscr.com/image/785c83b452c742bd851c0620d89a0b7a.png and
http://image.prntscr.com/image/66250909ff8b4a72b19b6ba634e58ab7.png

After this, Please go to your Admin Dashboard > Appearance > Customize > Menus > Menu Locations and assign the created menu to top menu and social menu location respectively.

Then verify whether you have checked the option to show the social icon by going to Admin Dashboard > Appearance > Customize > Theme Options>Header Options.

social Icons.
http://image.prntscr.com/image/2faa0fd03159485f82298b68e5b8ae65.png

Hope this helps,
If you have any problem while achieving this result, please let us know.

Best Regards !!

Hello @shotokan-test,

Glad we could help you !!

If you have any issues further, please feel free to post your queries and we will happily help you further.

We will really appreciate if you could help us too by rating our theme in WordPress repo here:-

https://wordpress.org/support/theme/magazine-plus/reviews/

Best regards !!