The commenter must use the embed code from Youtube? If so, this won't be obvious to the commenters.
No the users just need to copy the URL and paste it in the comment content. You can check it here: http://wpdiscuz.com/addons/wpdiscuz-media-uploader/#comments
Please navigate to Dashboard > Comments > Settings > Addons > Uploader admin page, make sure the "Allow media embedding function" is enabled.
Also, is there a way to make links open in a new browser tab? As it is now, it redirects the visitor to a new website.
Please put the following js code in your active theme js file:
jQuery('#wpcomm .wc-comment-text a').attr('target', '_blank');
Here is an instruction you can use: https://www.ostraining.com/blog/wordpress/custom-js/