Display 3 recent posts from one taxonomy

You should use Taxonomy Parameters available in WP_Query. For example, to get the three recents magazine_entry posts having the international term slug, you can use:

$args = array(
    'post_type' => 'magazine_entry',
    'posts_per_page' => 3
    'tax_query' => array(
        array(
            'taxonomy' => 'division',
            'field' => 'slug',
            'terms' => 'international'
        )
    )
);
$query = new WP_Query( $args );