Product Search

I've setup the joomla search such that it searches and finds the products and categories in my shop. But it also displays the non-shop pages around the site on the same words. Can you setup the search to just search the shop and not the whole site?

Yes, you need to unpublish the other search plugins in the joomla plugins manager.

So no way to have a full site search then a separate store search?

You can. In that case, you should use a filter for your products:
www.hikashop.com/en/support/documentatio...-filter-listing.html
and not use the hikashop search plugins.

You woudl then have two separate places to search on your website.