automatically make a group jive group on sign up

How do I code a new member automatically makes a group jive group on sign up named the users username?

Then would it be possible to have the subscription plan invite email linked to the family member plan that is sent out to be DESIGNED and have a INVITE link to join the group jive group of the invite? cb_username this way the new user and invite would have a connection from the invite email?
Thanks
Or could the new user invited be automatically assigned to the invitation groupjive group while/when accepting the invitation email?

Thanks

How do I code a new member automatically makes a group jive group on sign up named the users username?

You should be able to use a CB GroupJive action in CB Auto Actions for that acting on onAfterNewUser (backend) and onAfterUserRegistration (frontend) registration triggers.

Then would it be possible to have the subscription plan invite email linked to the family member plan that is sent out to be DESIGNED and have a INVITE link to join the group jive group of the invite? cb_username this way the new user and invite would have a connection from the invite email?
Thanks
Or could the new user invited be automatically assigned to the invitation groupjive group while/when accepting the invitation email?

Group invites have nothing to do with connections so I'm not sure what you mean by making them connected like that. You can customize the family plan emails directly in the family plan parameters while editing your plan.