displaying recent comments outside loop without plugin

You can do that with get_comments.

<?php
$comments = get_comments(array(
    'number'      => 10, // 10 comments
    'status'      => 'approve', // only approved comments
    'post_status' => 'publish', // only on published posts
));

// do stuff with $comments

You can see how the core itself does this in the recent comments widget.