1. How to edit the Transparent Header (seen on Homepage)
2. How to edit the solid-colour Header (seen on the inner pages)
3. How to edit the logo image
You can edit the column and the Site Logo styles:
To set the logo size, visit the Style section:
You can edit the Logo image, Site title and Tagline in Customize > Site identity:
You can check this guide for more details: Vamtam Elementor Themes: How to edit the Logo image, Site Title and Tagline?
2. How to edit the menu/navigation
Click the "Edit column" icon to edit the navigation background, borders and layout.
Click the "Edit Nav Menu" icon to select the menu and edit the navigation styles and layout. The Lagar theme has two menu positions left and right - you have to set the menu for both locations.
3. How to edit / remove the search icon
Click the "Edit Menu Cart" icon to edit the element's icon, alignment, styles, etc.
You can also check this guide: How to edit the Cart overlay background colour? - Lagar Elementor Theme
Editing the header for mobile resolution
Switch between Desktop, Mobile or Tablet views by clicking on the corresponding icons on the bottom of the panel and edit the content dedicated to the corresponding resolution:
You can also check this instruction: https://elementor.com/help/mobile-editing/