The look she had when she saw the Project Wideawake file could mean many different things. Yes, like you (apparently), I took it to mean that she felt something for the loss of these characters, and the fact that I am aware of how she and Azazel are Kurt's parents in the comic made me think that that emotion was aimed more so at the photo of Azazel.
But that doesn't necessarily have to be the case.
We do know that one of Azazel's powers (in the comics) is to be able to metamorph, so that could be used as a plot element.
But yes, in the comics, it was explained that Mystique was in love with Azazel and that he was actually in love with her as well, making her the only person that he ever truly loved. This is what led to her cheating on her husband, Baron Christian Wagner.
But with Azazel being dead they could do whatever they want with the reasoning of why they ended up mating in order to fit this story. And whatever they do decide it can easily be explained in this movie!
Yes, I agree with you that it would have been known by Mystique that Erik was imprisoned, but I'm pretty sure the wheareabouts were kept secret. Maybe the reason why she had to give baby Kurt up was that she went on a mission to try to find Erik.
And yes, they don't have to have been lovers in order for her to join his side, but I believe it's safe to say that most people believe that Erik and Raven were and continued to be lovers after she left the X-Men and joined Erik's Brotherhood: