Gallery Shortcode Showing IDs

Remove:

$content = get_the_content();

and replace:

<p><?php echo $content; ?></p>

with:

<?php the_content(); ?>

See this note on the Codex page for get_the_content():

An important difference from the_content() is that get_the_content() does not pass the content through the ‘the_content’ filters. This means that get_the_content() will not auto-embed videos or expand shortcodes, among other things.