She would like to disable those notifications, but I don't know how to do that for her.
You can't do that for her, but she can do it herself. If she is a WordPress.com user and selected the follow comment option while logged in, she should go to the Reader and click Edit next to Blogs I Follow. She should then click the edit link next to your blog and disable comment notifications for your blog: http://en.support.wordpress.com/following/#manage-email-and-im-settings-for-specific-blogs
If she is not a WordPress user and supplied her email to follow comments, she should use the unsubscribe link which appears at the bottom of the notification email: http://en.support.wordpress.com/following-comments/#managing-post-comment-notification
Also, anytime I tag one of my own previous posts in a new post, it treats it as a comment. Is there a way to avoid that?
This is called a pingback and is generated automatically whenever you link to an existing post or page on WordPress.com, be it on your own site or someone else's. This is actually a good thing as it creates a link between related posts on your site and will enable visitors to the old post to also find the new related one.
However, if you don't want pingbacks to appear on your own older posts, simply backlink to them using the short URL you can get by hovering the mouse over the blog title in the black admin bar. If you use the shortlink rather than the full URL from the address bar, it won't trigger a pingback. You can also edit the full URL as explained in this support doc: http://en.support.wordpress.com/comments/pingbacks/