Hi Pamela,
Thank you for the log-in details, it helped me a lot.
I think I managed to find the file responsible of printing that header search. I have replaced their form, with the search shortcode. The file changed was in the theme folders within the wp-content/themes/kalium/inc/laborator_functions.php. Please make sure to have a copy of it. I used search instance = 4 aka ‘Main search’ for that replacement.
I have also made some adjustments under the Layout Options -> Compact layout panel for better search visibility: https://i.imgur.com/TkhmNpa.png
Please note, that his qualifies as a customization request, so my solution may not work in 100% of the cases.
Thank you for the screenshot, I think you are looking for the front-end filters, this documentation may help you out: Front-end Filters