Hi!
I think you are reffering to results templating, the custom template files you created are probably located under the asp folder in the child theme directory.
The auto populate feature is the other thing you are looking for.
The pagination is printed within the wp-content/plugins/ajax-search-pro/includes/views/asp.shortcode.results.php file. However I do not recommend changing it’s structure, as it may not register with the pagination script directly. If you need styling changes, then I rather recommend using custom CSS.