Hello,
1. Browse categories: create your category menu in Appearance > Menu, then add Category element in Header builder and choose the proper menu form the drop-down.
2. Main menu: Appearance > Menu > set is as Main in the bottom and shows it with Main menu element.
3. Purchase theme: Appearance > Menu > and show it with the Secondary menu element.
4. Search is configured in the Header builder by means of search element, you can configure categories in the search.
Best Regards