How to get list of custom taxonomy terms and display count?

This is actually a three-part question.

1.) How do I get list all terms of my custom taxonomy (in this case, ‘audiocat’)?

2.) How do I display the count of each term? Example:

Rock (5)
Pop (3)

3.) How do I sort them according to their parent? Example:

Rock (5)
  Subcategory (3)
Pop (3)
  Sub category (1)

So far, I can get the list of all the terms from ‘audiocat’ but if they have more than one content, then it duplicates it. So I can’t proceed to my second problem.

Here’s how I query them:

<?php
$audio = get_posts( array (
'paged' => get_query_var('paged'),
'post_type' => 'audio',
'posts_per_page' => 10,
'order' => 'ASC',
'orderby' => 'meta_value',
'taxonomy' => 'audiocat',
));
?>