How to callback custom field text

Your text is already in the array $m_slider_custom, from this line:

$m_slider_custom = get_post_custom($post->ID);

If you just want the specific key feat_music you can use get_post_meta():

echo get_post_meta( $post->ID, 'feat_music', true );

Another, unrelated thing- I suggest spending some time with the Codex and cleaning up your URLs and paths. For example, this:

get_option('siteurl') . '/wp-admin/admin.php?page=rated-featured-music/options.php';

or this:

get_bloginfo('url') . '/wp-content/plugins/rated-featured-music/scripts/jquery.cycle.all.2.72.js'

or this:

include (ABSPATH . '/wp-content/plugins/rated-featured-music/content-slider.php');

.. will fail spectacularly under certain circumstances. WordPress has built in functions for getting any path or URL you’d need, see:

http://codex.wordpress.org/Function_Reference/admin_url
http://codex.wordpress.org/Function_Reference/plugins_url
http://codex.wordpress.org/Function_Reference/plugin_dir_path