Search functionality

I recently installed the Storebox template with all the demo content. I have not yet made any changes, other than updating a module and 2 components after the install. I did a basic test of searching for a product from the search box on the homepage. First, in the back end (administrator), I went to VirtueMart and clicked "Products". It lists 64 products, one which is named "St Anton Unisex Hat", which shows as "Published" (checked within the product details page). The item is displayed when I go through the Categories page on the site. However, on the homepage of the site, in the search box at the top, I entered "anton", which returned "0" results. I have a major problem with this if my site is a store and published items cannot be searched using the main search box on the homepage. Why did this search return 0 results when the item exists in the store?

Hi,
but what is important, GK didn't developed any search mechanism for VM3 extension.
So probably you will get this same "0" result on default Joomla template, you can easily check it

Is there a way to incorporate the Storebox search and the Virtuemart search module? I only want one search box at the top of the page that can search everything and would like it to look like the Storebox search box with the magnifying glass icon!

You have two options:
1 - make it using a CSS and font awesome icon or graphic icon
2 - install module search module which already have this appearance or even more for example Ajax search