szaval,
Thanks for sending me the URL to look at.
There's a few issues, I think, but we'll need to take care of them one at a time. On the category layout, you're using JFBConnect's Like button. However, when I click into a category ("David", for instance), the Like button at the top there is not coming from JFBConnect. I'm not sure what extension that is (it may be K2's built in Like buttons), but you should use the same extension's Like buttons for both the category listing view and the individual categories themselves. Each extension can create the URL a little differently, but what's most important is that they are consistent.
Hopefully, you can enable JFBConnect's Like buttons in the Item view, and that will fix most of your problems. If not, just let us know!
Thanks,
Alex