Charalampos,
Glad you found the issue with Disqus. The problem was likely that they were re-adding Open Graph tags, which describe your page to Facebook, and doing so in a conflicting way with JFBConnect.
As for the posting to Facebook, the Like was likely put into your Timeline, but it may not be prominently shown in their feed. If you go to Facebook and click on the "Activity Log" button in the bottom right of your cover photo, you may see the Like action there. It may not show up in your Timeline due to several social factors based on the viewer of your feed, including your self.
One thing to help make sure the image is posted is to specify the image for the page. This can be done by enabling our Open Graph plugins for content, k2, easyblog, etc, which will try to automatically select an image for those components. Or, in the article area, you can add {SCOpenGraph image=http://yoursite.com/link-to-an-image.jpg} to specify a specific image for that article. Finally, in the Open Graph -> Settings area, you can set a default image (like a logo) to use across your whole site in case an image hasn't been added otherwise.
Hope that helps explain, but if you need more help, just let us know.
Thanks,
Alex