1 - A teaser forum is just a plain, ordinary forum. Like any other forum, it appears in a single category, and its visibility to Admins, Mods, User, Guests or other groups is determined by whatever you specify in the forum's settings.
2 - I suspect that would be messy to implement. A easier alternative would be an IIP box or IIP Sidebar box. The IIP news box pal could be used as a starting point.