How to show category images (from plugin) on a regular page (page-example.php)?

Untested, but something like this should work.

$siteurl = home_url("https://wordpress.stackexchange.com/");
$tax = 'region';  // slug of taxonomy
$terms = get_terms($tax);
foreach ($terms as $term) {
    $id = $term->term_id;
    $slug = $term->slug;
    $description = $term->description;
    $image_url = z_taxonomy_image_url( $id, NULL, TRUE );
    $link = "<a href="https://wordpress.stackexchange.com/questions/176555/$siteurl?$tax=$slug" ><h1> $term->name </h1></a>";

    echo $link;
    echo '<p>' . $description . '</p>';
    echo '<img src="' . $image_url . '">';
}

2nd argument of z_taxonomy_image_url() is image size and 3rd argument is for returning placeholder image.