How to get custom category’s link?

As the other’s mentioned, wp_list_categories will work if you you want to do a list of things (just like wp_list_pages does for pages).

If you specifically want the link (URL), you can use get_term_link. If you just have the term ID, it would look something like this.

<?php
$term_id = some_function_that_returns_term_id();
$term_link = get_term_link($term_id, 'your_custom_taxonomy');

if (!is_wp_error($term_link)) {
    // do stuff with $term_link
}

If you have the whole term object — for example the object returned by get_term_by — you can pass the entire object in as the first argument of get_term_link and you’re done.

<?php
$term = get_term_by('id', $some_term_id, 'your_custom_taxonomy');

$term_link = false;
if ($term) {
    $term_link = get_term_link($term);
}

if (!is_wp_error($term_link)) {
    // do stuff with $term_link
}