Get all media files for current author

Media are just posts – so just query posts. This is untested:

$args = array(
    'author' => $author_id,
    'post_type' => 'attachment',
);
$query = new WP_Query( $args );

I’m not sure if you want currently logged in user or the author of the post currently in the loop – either way you can set $author_id above appropriately.