Hi,
Unfortunately, it is not possible to change the behavior of the search form without additional code customization. There are no such options in our theme.
For the fatal error in the search bar please once make sure your WoodMart theme and Core plugin is updated to the latest version and then check back the issue again on your Site. If it is not updated then you can update the Theme and Core following the Documentation Guide:
https://xtemos.com/docs-topic/update-the-theme/
If the issue still persists after updating the Theme and Core plugin, then could you please once try deactivating all the third party Plugins on your Site, remaining the Theme required ones activated. If the issue gets resolved, then reactivate them one by one to see which Plugin is causing the issue. If this doesn’t work for you then once also, try to activate the Parent Theme on your Site if you are using Child Theme on your Site.
If somehow the issue still persists, then please take complete Backup of your Site first, then provide us the WP-ADMIN Login details of your Site in the Private Content field along with the permission to completely debug your Site which includes deactivating all the third party Plugins and removal of on-Site Customization changes too, so that we can thoroughly check this issue on your Site and assist you accordingly.
Best Regards.