Carlos,
1) Yes, you can set JFBConnect up in a "Normal" registration mode where the user can choose their own username and password during the registration process. The automatic registration mode is what we use here, but it's not necessary.
2) Existing users can connect in a few ways. With the Normal Registration mode, after the user clicks the Login With Facebook button, they will be brought to a page where they can create a new account *or* login to an existing Joomla account. If they login, that will connect their Joomla account to their Facebook one.
Also, JFBConnect can be setup to automatically link existing users if their Facebook email address is the same as their existing Joomla account. That makes connection a 1-click process.
3) Yes, you can import the users avatar and other profile information into Kunena. You can also configure JFBConnect to only import the user's profile if the user is registering. Then, if the users are just logging in or connecting accounts, the avatar will not be overridden.
The admin configuration area can be seen on our demo site if you want to test the settings from #1 and #2. We don't have Kunena installed on the demo site, but you can get a good feel for how it works:
demo.sourcecoast.com
Hope that all helps, but if you have any questions, just let us know.
Alex