Hello,
Please go to Appearance > Customize > Header > Mobile Menu, from here try to set the element positioning as Link/Logo/Cart.
https://ibb.co/n0Jt4Qg
For the search icon, that is inside of the mobile menu, and unfortunately, no settings to display that icon outside of the menu.
But there is a way, you can try the custom header style in which you can put each header elements according to your need for desktop and mobile both.
Following the doc will help you with it.
https://docs.oceanwp.org/article/355-how-to-create-a-custom-header