Is it possible to select and edit the way the most recent post from a certain category is displayed on the page?

Question

You can retrieve the index of the post in the loop with $wp_query->current_post. From that, you can check with a simple if-statement:

/*Check if post index is 2 (you referred to the 3rd post, given indexing starts from 0, the 3rd post index would be 2 */
if ( $wp_query->current_post == 2 ) : 
   /* Do something */
else:
   /* Do something else */
endif;