The new mail notification shows up whenever there's a new email in your inbox, it's part of the app itself, not a plugin or anything. About Push, it depends on what type of email account you have. If it is a Yahoo account, for example, then it should appear in Mail the moment the other person sends it. For me, I have a Gmail account so I've set my Mail app to fetch new mail every minute...it's the closest thing I can get to push on my Mac at the moment.