Make sure that you're using the latest version of the theme, this sentence should be translatable. If it doesn't work in you case you can try to translate it by modifying the php file directly. Open up wp-content\themes\brightbox\framework\php\function-set-avia-frontend.php and search for following code:
if(!empty($wp_query->found_posts))
{
if($wp_query->found_posts > 1)
{
$output = $wp_query->found_posts ." ". __('search results for: ','avia_framework').esc_attr($_GET['s']);
}
else
{
$output = $wp_query->found_posts ." ". __('search result for: ','avia_framework').esc_attr($_GET['s']);
}
}
else
{
$output = __('Search results for: ','avia_framework').esc_attr($_GET['s']);
}
Then replace "search result for" with your custom text.
Brightbox does not support the breadcrumbs at the moment.