There is only one super admin that can create groups, he can also create users.

Group creation can be limited globally or category based to specific usergroups, very doable.

The super user can give each group a admin.

Groups have the following usertypes:

Owner
Active
Inactive (needs approval)
Banned

The group admin can create users for his group.

Forcing users to groups can only be done from backend, sorry. Those admins could "invite" users to join a group however, but is purely optional.

Users can not create themselfs, they must be created by the super admin or the group admin.

Suppose you could set all groups to "Invite" type requiring them to be invited into a group.

Not likely, there is code in place to prevent phishing, spam, or unauthorized addition of users. You'll need a new integration that uses GJ API to add users correctly.

GroupJive is groups similar to groups seen on Facebook, MySpace, and many other social sites. It's nothing beyond that. It can be customized in the way that names can be changed so for example "Groups" can be renamed to "Companies" and have the same group like features, but different subject. If this is what you're needing it'll certainly fit the bill. You may want to review other social sites to grasp what GJ would be like. You can also try it out at our demo site below.

cbsubs1.cbdemosites.com/cb-groupjive