Search form not working

It looks like only query and category params are not working, this is some kind of conflict with your theme you should be able to fix it by:

1. add in your theme functions.php file the code below

add_filter( "adverts_form_load", "change_query_field_name" );
function change_query_field_name( $form ) {
  if( $form['name'] != "search" ) {
    return $form;
  }
  foreach( $form["field"] as $key => $field ) {
    if( $field["name"] == "query" ) {
        $form["field"][$key]["name"] = "ad_query";
    }
  }
  return $form;
}
add_filter( "adverts_list_query", function( $args ) {
  if( adverts_request( "ad_query" ) ) {
    $args["s"] = adverts_request( "ad_query" );
  }
  return $args;
});

2. edit the search-by-category.php snippet and on line 28, 54, 62 change advert_category to ad_category.

Where I find the search-by-category.php snippet?

It depends on how you have it added on site, usually, it should be in wp-admin / Plugins panel (in the file system that would be wp-content/plugins/search-by-category) or the code can be copied and pasted in your theme functions.php file.

Unless you have the Category field added using Custom Fields extension, then the code will not be anywhere, and you will just need to rename the Category field using Custom Fields editor.

Ok, thank you!