Sounds like a basic affiliation system. I've no idea what you mean by give credit though; Points? Money? CB Invites will allow your users to send an invite to an email address and when the invite is accepted the user that sent the invite will see this on their profile. You could even have them become connected using CB Connections automatically when the invite is accepted.

is it possible to see those connections on the back-end or front-end by the administrator?

No, connections is frontend only.

How can I make cb connections to connect automatically when they accept the invite?

CB > Plugin Management > CB Invites > Config > Invites > General > "Connection".

One of the challenge I have is for the system to connect automatically (as you said) whether the leader is register or not. It does not make sense if leader is not register yet but when he does is there a way to do it??

I don't understand. I thought the whole point was for the leader to invite others to join the site. That's exactly what CB Invites can do and even connect them together if CB Connections is used. No someone that isn't even on the site can't invite someone to join the site, there's no one to associate the registered user with.

maybe by using a username? Member could type username leader and when this username had register it could automatically connect to their team.

You don't need to do that. The leader could just use CB Invites to invite the Member to join the site. When that Member joins their registration will accept the invite and if enabled be automatically connected to the Leader. Aside from that yeah I guess you could have a field for them to supply username or user_id, but beyond that it's just a field and what you do with it is up to you.

We'll you could use the CB DB Lookup field to ensure the username they supply actually exists on your site. Beyond that you'll need to develop something or try using CB Auto Actions to create a connection between the two. We've really nothing in place for this. Best approach is to have the Leader invite others using CB Invites otherwise you've no idea who is associated with who and there's nothing in place to enforce that.