Are you talking about Office 365 groups or distro groups? Either way, Teams won't have a Team tied to those just by moving unless you specifically create a Team on that Office 365 group. So nothing technically changes by moving to Teams from Skype other than your chat happens in the Teams client, and your meetings are all handled there.
You then have to create Teams in the client (Or admin center) for people to join and collaborate if they want too. You have 2 options. Create a Team from an existing Office 365 group, or Create a new Team, which creates a new Office 365 group with the Team attached (including SharePoint Site). When you create a new Team the group is also hidden from Outlook and Address book.
1. No 2. Nothing changes unless you create Teams and add people to them, as above either from existing 365 group or new Team (new group) 3. Teams really is a real time collab app different than e-mail, it just really uses the Groups back end for security / mail storage for compliance, and to a smaller effect meeting invites for channel meetings etc. but tha'ts a mess right now. 4. hopefully nothing now with my explanation :).
Thanks for the speedy, point-by-point response. Although I'm aware of much of what you said, you clarified and confirmed several things.
My reference to Groups was to Office 365 Groups, not distro groups.
Putting aside the transition away from S4B....as others do, I differentiate Teams from Groups primarily by the way communications and associated documents are handled; in Groups it's email and a classic SharePoint library; in Teams, it's persistent chat and channels (though SharePoint plays a role there, too).
In our case, there is a generational factor. Since all my users are over 50 years old (even an octogenarian or two), chat and channels don't come naturally, email is an old friend, and change in general is especially difficult. So, we've stuck with Groups so far. Even the only cohort inadvertently organized as a Team, our staff, uses email and SharePoint, ignoring the availability of chat and channels. I'm always on the lookout for an opportunity to expand their use of Teams' features, and they may be on the cusp of exploring chat/channels.