Customize Theme Header Storefront

Hello,

I would like to customize the header of the woocommerce theme storefront. The logo should be on the top left, the menu on the top right, the cart underneath the menu.

Storefront creates divs with the class col-full which uses the full width of the container. Is it possible to add customised classes or change otherwise the structure of this area?

Thanks

The page I need help with: [log in to see the link]