display one post out of each custom category (aka “term of custom taxonomy”)

You can use tax_query to query your posts based on the taxonomy. But be advised, if you have a lot of categories, then this is gonna take a lot of resources, unless you use a cache plugin.

$terms = get_terms(array('taxonomy' => 'album', 'exclude' => 4)); 
foreach ($terms as $term){
    $args = array(
    'post_type' => 'simple_image', 
    'posts_per_page' => '1',
    'order_by' => 'date', 
    'order' => 'ASC', 
    'tax_query' => array(
        array(
            'taxonomy' => 'album',
            'field' => 'slug',
            'terms' => $term->slug, 
            )
        )
    );
    $new_query = new WP_Query ($args);
    if ($new_query->have_posts()) {
        while($new_query->have_posts()){
            $new_query->the_post();
            the_post_thumbnail('thumbnail');
        }
    }
    wp_reset_postdata();
}

As you have already noticed, this will run 100 queries, if you have 100 terms under that taxonomy. So, make sure you use it in conjunction with a cache plugin.