1- Registration Capabilities with custom Fields - CB or CB PRO?

There is no CB Pro. There's just CB. The professional subscription gives access to additional plugins for CB. The core CB it self is free and comes with its core fields built in.

2- Ability to redirect user to complete profile. I want to have limited signup fields but after signup to redirect user to complete their profile. Which Product will support this need?

After registering they'll need to confirm their account and/or be approved by a moderator if enabled. They can then login and begin editing their profile. Core CB lets you specify a login redirect in addition to first time login redirect, which you could set to the profile edit URL.

3- Ability to redirect user after sign up to a form to invite fiends to join the site. Which Product will support this need?

You need CB Invites for this, which is managed entirely from their profile. See my above reply regarding redirect.

3- Ability to open the site to certain sections depending on how many of his invited friends have joined the site. Which Product will support this need?

We don't have anything that provides such functionality. Best you could do is limit access to fields/tabs using CB Conditionals, but outside of CB you won't be able to do this unless those locations provide such functionality.