Comments Everywhere is a plugin that enables you to insert a comment section where you want by using a shortcode.
When you place the shortcode a post_id gets generated using the uid you passed. This id is used to mimic a post or page and insert a comment form and the comments.
No, the generated id is such a large number, you would have to write millions of posts.
When you want to insert comments on a particular page, or custom template etc.
Yes another reason to use the plugin is the abaility to modify the comment template, as the plugin uses its own file for the template.