Commerce Kickstart change full text search product display to https
Maintainer of Commerce Kickstart.

I just checked out the site, and it's using a relative path like Drupal forms are expected to do. From your source:

&lt;form action="/products" method="get" id="views-exposed-form-display-products-page" accept-charset="UTF-8"&gt;


The search form is a Views exposed filter exposed as a block. There isn't much trickery going on with the form beyond typical site building.

Also, I did not get mixed content warnings.