How to display custom taxonomy and terms using/creating plugin template

In the taxonomy-user_image_category.php the get_queried_object method will return the term object, which you can incorporate to your WP_Query. From top of my head, in your case it may look like this:

$queried_object = get_queried_object();
$term_id = $queried_object->term_id;

$args = array(
  'post_type' => 'user_images',
  'post_status' => 'publish',
  'tax_query' => array(
      array(
          'taxonomy' => 'sui_image_category',
          'field' => 'id',
          'terms' => $term_id
      )
   )
);

$posts = new WP_Query($args);