The main issue was that your <button> for mobile didn't have name="Search" and your search uses that as the trigger.
Another issue is that you had a <label> tag wrapping both the button and input, which caused iphones to immediately submit when focus was put into the input field.
A third issue is that your top.php include has doctype and head tags and so did your page causing invalid html.
I fixed all of those issues on your products_results-search.php page, but you would have to update the position of the top.php page similarly on other pages.