Hi!
1. Yes – the option is a little bit tucked away, but you can turn it off here: https://i.imgur.com/FLDNzoD.png
2. Surely! If you use the search shortcode/module/widget in a page or somewhere in a page builder, then of course the simplest way is to add a heading/paragraph module above it and write the title. I assume that is not possible in your case.
There is still a chance programmatically:
add_action(
'asp_layout_before_shortcode',
function () {
?>
<h2>Title here</h2>
<?php
}
);
Try adding this code via the Code Snippets plugin or 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.