I would like the code and where to implement it so that when searching for blog posts, the search result shows the featured image of the post along with the title, date, and author when the enter or search button is pressed. Thank you.
I recommend using the theme functions feature within the theme you are using. With that you can fetch the additional information (such as the featured image) parsed by Ajax Search Pro, and use it within the template, in the search results loop.
You may have to ask the theme author about that – it is usually different for each and every theme out there. Unfortunately there is no specific location. For basic themes it is the search.php file, but it can be within the archive templates, loop files or nearly anywhere.
I don’t know if anything like that exists, because it depends on the theme structure. You can check the official WordPress documentation on it, but it is only a very basic tutorial for a specific basic theme.