Creating a custom top menu in Bridge Theme

I would like to create a top menu like the one on this page.

The menu interacts with the mobile device as well.

For the desktop, the spacing for half the menu is on the left with the logo and the other half of the menu on the right. Additionally, there is some custom code that is creating a button type of environment for the last and second to last item, but it disappears once it transfers to the mobile device.

The site I am trying to transfer it to is which is using the bridge theme.

I currently have added some buttons to the “header bottom right” widget, but the menu is gone when I go to the mobile. Can anyone help me figure this out?