Pop up for registration poping up (very briefly) during login after FB

If the popup displays and dissappears right away, that's normal. It means the following:
* You are already logged into Facebook.com
* The user you are logged in with has already approved the Facebook Application you created for your site and granted all the permissions necessary
Because of that, the popup automatically disappears and you should be logged in as expected.

It is a problem since my app always crashes after getting a pop-up from JFB Connect.

What do you mean 'crashes'? If you're seeing a blank white page, please set Error Reporting to 'maximum' in the Joomla -> Global Configuration area. That should show an error message which will help narrow things down. If you mean something else, please explain further so we can help understand the issue.

Thanks,
Alex

however only on the application.

I'm not sure what you mean by this. Is this when you view through a Facebook Canvas area only, or something else?

Let me try to find out what the problem is and how I can see what the problem is (never done error reporting stuff on an app).

Generally, just enabling the Error Reporting setting in the Global Configuration area is the only step necessary. If you are getting a white page, that setting should show a message as to the cause of the white page. Tell us that error message, and we'll know what to do next. You shouldn't need to go digging around much.

Of course, any other details on your configuration or setup is always helpful so that we know exactly how you're configuring JFBConnect and what you're trying to do.

Thanks,
Alex