But I would also like the user to be able to choose to register manually or using facebook credentials - is that possible too ? So that users without Facebook profile also can register on the website.
I don't understand what you're trying to do. If you want their Facebook data to popular your registration form you use pre-filled mode otherwise use single sign-on which will register and login them automatically. You can map additional Facebook profile data within CB Connect parameters, but what information is available is limited and not guaranteed.
I believe there is something wrong here!! The real name of the column in the database is cb_fb_userid not fb_userid ???? Is this a bug in the plugin ?
That's a known issue with CB it self. Install latest CB 2.x nightly then re-install CB Connect and the proper fields should be created.