Perfect, that helped.
I created the suggested file for you, you can find it in: home\dh_dzvjxp\thenobo.com\wp-content\themes\elessi-theme-child\includes\nasa-mobile-product-searchform.php
Yes, you can create a different search bar, and use that shortcode there. The plugin shortcode is placed on line 34 in that file, you only need to change the id=1 part of it, to the ID of the desired search bar.