Will I know when there are new subscribers (and 'un'subscribers)?
Yes. In the TFMail reporting tool, the number of un/subscribers are available per week, month and year, as well as per mailshot sent.

Why does my subscribe/unsubscribe form not list an “unsubscribe” option at the bottom when more than one list is selected?
If your client is subscribed to more than one list then the subscribe list will show which lists their subscribed to. If they wish to unsubscribe from one of those lists they must uncheck that list and then click on the “Update” link. If they wish to unsubscribe from all you lists they must click on the “Unsubscribe All” link.