What you need would require a lot of custom coding/development with X. The good news is you can upgrade to Pro which includes a Header and Footer builder and you can easily build your header design. Here's how to upgrade: https://theme.co/apex/forum/t/x-to-pro-conversion/104
After you upgrade, go to Pro > Templates and import the Starter Pack.
That will import the Starter: Logo Middle Header Template. You can use that template when creating headers.
Here's the look of the template. Change the parts to make it your own. You need to set up 2 menus in Appearance > Menus by the way.
You can learn more about Pro in our Knowledge Base and Youtube channel.
Please note that we do not offer custom development as part of our theme support. If you wish to proceed with your header design with X, you'd regretfully need to hire a web developer.
Hope that helps and thank you for understanding.