What options are available for receiving an email when a particular tag is added or updated? More broadly what options exist if any for receiving an email when a people field such as member status is changed?
That depends on what kind of tag you are talking about. Event tags have an option called Notify Owner but I believe that only exists in Events.
I think it would be quite overwhelming to your inbox to receive that many notifications, but you could consider using a report grid from query to display the people who have been changed or added to a tag, or using report services to email you a report that contains that information at a specific time of the day.
when you say report services are you referencing SSRS?