Well, that “link back” might be a Trackback or Pingback. It´s a function to inform other blogs that you have “used”, mentioned or linked to their content. It´s made for connecting blogs with each other.
Some themes show Track-/Pingbacks in the comment section, some don´t. Anyway, if you want to disable them, you can do so under Settings -> Discussion -> “Allow link notifications from other weblogs” (Don´t know the full translation, I am using WP in German, anyway second point from the top).
Your facebook comments are a whole different topic.
They are completely managed by Facebook and only linked through the Facebook comments plugin. You have to manage them right through that plugin in that case and they won´t show up in the WordPress Dashboard/Comments section.
Possibly there are plugins to notify you or list comments that are made via that Facebook plugin, but I don´t know that plugin, possibly someone else can help on that.