As an Owner of a Google Group you can add any member with an email address using the "Manage - Direct Add" option . The "Manage - Invite member" option can only be used to invite members with VCU faculty or staff email address.
If we haven't yet switched you to the new Google Groups, you can switch yourself. Just go to Groups and click the Switch to the new Google Groups link at the top of the page.
Yes. Check out these easy-to-follow guides for creating and using the new Google Groups—as email lists, Q&A forums, web forums, and collaborative inboxes.
Note: You might need to work with a group owner or manager, or your Google Apps administrator to enable all the new features.
Yes. Eventually the new version of Groups will become permanent and you won't be able to switch back to the classic version of Groups. But hopefully you'll have had enough time to get used to the changes!