Pull most commented and liked pictures from your Facebook Profile or Page you manage and display them in your sidebar or any widgetized area.
Sure you can. You'll have to use the global variable $fbdata and call either the $fbdata->get_pictures($amount, $offset) method for pictures or $fbdata->get_albums($amount) for albums. This will return an array containing the data, that you can display and style as needed.
It really depends on how many pictures you have on your Facebook account: the more pictures, the more it takes Facebook to give us the information we need. In any case, data is stored on your site for 24 hours, so worst case scenario you'll see a load delay on one pageview every day.