To be honest this is a tough one I remember one of my friends when we started hanging out she willingly gave me her email password as a "good will gesture." I dont really care who talks to any of the females I am talking to because I am not committed but once when she was over she insisted we go through it. Now the number of guys sending pictures of themselves wacking one out, or just naked or whatever was crazy. Now this is a freaky girl she is highly sexed and im sure some of the guys she sent back naked pictures etc but it seems to be common now for guys to do this. (Dont ask me why).
Your situation differs because you are in a relationship living with the woman now are these just the same type of guys who think its sexy to send this sort of thing? Or are they guys who know she is turned on by this and likely to respond in a positive manner?. Only you know, you know your girl. Regardless of what advice you get on here its you who knows how she is and how she responds in most given situations. What would I do?. In your situation there are obvious emotions and attachments so you really should have played Sherlock for a while but its too late. I dont think attacking the guy was the right response as guys usually try and sleep with everyone.
This is where I will get slagged off but why do people in relationships have private facebooks?. I mean if you share a home, family, children, bank accounts you know each others secrets, right?. I think you put any human being in a situation under the right conditions anything can happen. Women are not these perfect, faithful creatures that most men think they are. They are even more deceptive, cunning and capable of doing things men would never think of. I wouldnt want my partner having a private page.
Not much you can do now so just good luck in the future.