User blog comment:IamJakuhoRaikoben/Chapter 402: Iron Fist of the Fire Dragon, Review./@comment-1359322-20140929144423/@comment-7418318-20141001214743

In regards to "how could they know" questions and similar, Cobra is pretty much a Deus Ex Machina.

Everyone of your questions about if they knew something or how can be answered with "cobra might have heard it out of someone's thoughts".

He knew that the Tartarus members are Demons from Zeref's book and that they were about to make their move, so he might also have learned about Project Face. Since they are all mages, losing their magic isn't something they'd want to happen.

And Jellal is stewing so much in his own guilt that I'm sure the truth about how he became "guilty" is pretty obvious to Cobra the moment Jellal's defense against that ability slips for a moment (I assume he has a defence, since he was able to defeat Cobra in a battle, which would have been very hard if his thoughts were laid bare) or Jellal might intentionally allow Cobra to read his thoughts, so he can show them the truth of his desire to free them, at which point Cobra might also glimpse some other tidbits.