Hi,
1. I’m afraid there is no option to do that, however you can modify the words displayed there via the asp_suggested_phrases hook.
2. That is an intended behavior, but there might be a way to trigger an empty search when clicking on the icon via a custom code.
Try adding this code to the functions.php file in your theme/child theme directory – make sure to have a full server back-up first for safety. For more details you can check the safe coding guidelines.
add_action('wp_footer', 'wp_footer_empty_on_close');
function wp_footer_empty_on_close() {
?>
<script>
jQuery(function($){
$('.asp_m .proclose svg').on('click touchend', function(e){
$(this).closest('.asp_m').find('input.orig').trigger('input');
});
});
</script>
<?php
}