Dynamic drop down of child terms and then drop down posts

For getting the child term of an parent you can use get_terms function

Here you can provide
hide_empty as false ( this will list all term )
parent as the parent term id ( this will return the term related to that parent id

$tax_id = $term->term_id; 
$terms = get_terms( 'post_tag', array(
    'hide_empty' => false,
    'parent'     => $tax_id,
) );