It sounds like there's an issue with the downloading of files from Facebook and storing them in that directory. If they are 0 bytes, then the directory is writable, but the information from Facebook didn't work for some reason.
Have you tried with other social networks, like Twitter, Google or LinkedIn? Knowing if the avatar and cover photo import from those will also help.
The main reason the images wouldn't download is due to a server issue with connecting to those networks and reading the data (either something is blocking the read, like a firewall, or the server isn't setup to follow specific redirects that the social networks use to locate their images). The best things to test further here are to:
* Set the Global Configuration -> Error Reporting option to 'Maximum'
* Set the 'Enable Debug Mode' In JFBConnect to 'Yes'
Then, when you authenticate, a better error message may display which can help explain the issue as well.
Let us know about either of the above questions and we'll do what we can to help get you going.
Thanks,
Alex