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 :).