Nothing's perfect, and in many cases, we're at the mercy of Facebook. They make changes and have plenty of their own implementation issues, which is what we spend a lot of our time 'working around'. Fortunately, most user's don't experience issues, but a few seem to experience more than their share, and are usually related to the same cause... in your case, a non-English language, which Facebook itself is mostly handling poorly, not JFBConnect, we're helping you get around their problems. Same with this avatar issue, they're responding with a non-secure image.
We just released version 3.1 of JFBConnect. While we don't think the updated version will fix your issues directly, it fixes and improves quite a few other areas.
As for the avatar itself, we're still investing a solution that we think should work for you. It will require a minor PHP code change to the JFBCLogin module if it works, but we're still unable to be certain that Facebook actually hosts the avatars on a secure CDN anywhere. From the reading we've done, they don't do this, which means there may not be a workaround.