Ajax Search Results styling / modification

Yes, you can.
If you are using default search template , then you can directly customize your search.php in your theme.

For ajax result template, you can use uwpqsf_result_tempt filter to customize the result. You can refer this post.

Nope, but you can implement it in the filter function:

function customize_output($results , $arg, $id, $getdata ){
	 // The Query
            $apiclass = new uwpqsfprocess();
             $query = new WP_Query( $arg );
		ob_start();	$result = '';
			// The Loop

		if ( $query->have_posts() ) {
			while ( $query->have_posts() ) {
				$query->the_post();global $post;
                                if($id == '123'){
                                   //include template for form 123
                                }elseif($id == '234'){
                                   //include template for form 234
                                }elseif ....
			}
                        echo  $apiclass->ajax_pagination($arg['paged'],$query->max_num_pages, 4, $id, $getdata);
		 } else {
					 echo  'no post found';
				}
				/* Restore original Post Data */
				wp_reset_postdata();

		$results = ob_get_clean();
			return $results;
}

You can use $id to identify the form, or use get_post_type($post->ID) for identify identify post’s post type in the while loop.