Hello Anna,
Thanks for writing to us.
To align the Contact envelope icon on the right side with social icon please add this custom CSS code under X-->Theme Option -->CSS
.x-topbar .p-info {
float: right;
}
Regretfully, there is no option to add a search bar in the top bar. It could be possible with custom development, but this would be outside the scope of support we can offer. You may wish to consult a developer to assist you with this. X is quite extensible with child themes, so there are plenty of possibilities.
This could be easily achieved with PRO instead of X. In PRO the You would get header builder to achieve your custom header layout.
The purpose of providing the custom CSS to show you how to add CSS code to your site. Writing custom CSS is outside the scope of our theme support. If you need more customization, you need to learn CSS and learn how to use the browser’s element inspector.
Thanks for understanding