Menu disappears on mobile and search Icon

In mobile, it will revert back to use the default Divi header, so that you can have slide in / fullscreen menu in mobile: https://divi.help/threads/for-mobile-menu-how-to-show-slide-in-or-fullscreen-menu.646/
**So if you wish to set the logo, set it in Divi > Theme Options > Logo.
**And to edit the mobile menu, go to Appearance > Menus & edit the Primary menu.
**And for the mobile menu background color, change it in Theme Customizer > Mobile Styles > Mobile Menu > Background Color.
**And for the hamburger color, change it in Theme Customizer > General Settings > Layout Settings > Theme Accent Color.

Nope. If you need the search icon, then you will need the menu module. If not, you can only use the Divi search bar module.

 

But if you wish to create your own Divi Builder mobile menu, then try to download the attached custom-mobile-menu.json file & import it in Divi Library. Then proceed to edit your custom header in Divi > DU Header - Library & add new section & load the Custom Mobile Menu.

Earlier, we just updated the .json in v2.0.1 to include the Custom Mobile Menu section.

But do note that if you use the Divi Builder mobile menu, then you can only have the default slide down menu style. But if you use the default Divi mobile header, then you can choose to have the slide in menu / fullscreen menu. That's why it's more recommended to use the default Divi header in mobile.