You can configure the header search field from the Appearance ▸ Customizing ▸ Brator Option ▸ Advanced Search Form
Use this below shortcode to set the search form anywhere on the site.
To get the correct result in the advanced search result you have to select the taxonomies for the product in every product one by one.
Also to keep the dependency of the taxonomies you have to configure the taxonomies…
And for the dependency in the search drop down you have to select these options in the theme options….