Hi,
The results page URL is requested from WordPress core, via the post/CPT ID. If you want to modify the results URLs, I recommend changing them on the post editor screen, so it is populated across the site.
However you can use a custom hook via asp_results if you want to edit the result URLs on the live results list.
After the plugin redirects to a single result page, it has no control of what is displayed there, that is defined within the theme, you will have to look in the theme options.