How to get all the items of a taxonomy even if it does not have a custom post type?

Question

Add a hide_empty argument:

$termsq = get_terms("competence",array('hide_empty'=>false));

See the Codex for the complete argument list.

Additionally, get_terms will return a WP_Error object on failure, so your count check won’t work. You need is_wp_error.

$termsq = get_terms("competence",array('hide_empty'=>false));
if (!is_wp_error($termsq)) {
  echo "<ul>";
  foreach ( $termsq as $termq ) {
    echo "<li>" . $termq->name . "</li>";
  }
  echo "</ul>";
}