His feelings for his ex can be a fleeting thing, or a long lasting issue that he continues to struggle with even now. Either way, it seems that he is struggling with his feelings, and is hiding this from his wife. This is the worst thing that can occur. By not discussing it openly and honestly, it keeps festering in him, and if he does not have a safe outlet, in time, it is possible that he may act on these feelings in an inappropriate way.
I think many of us still have some feelings for those we were in a past relationship with, however, you move on and start fresh with someone else. If one relationship ended prematurely, or seems to still be a presence in another relationship, that will create a lot of issues . Especially if it is not communicated or talked about with the new significant other.
Now, usually, I would dismiss the email to his ex, and facebook messages( sometimes those are from fake people, or advertisements,etc..) . Writing an email to an ex asking how they are, or asking another how they are, is innocent, and usually well meaning. I can't tell you how many times I have written to my ex's in high school, or they have written to me, and asked how things were doing. Usually we laugh when we find out we both are married with kids, thinking how old we are now, and such..
You had written that the husband cried and stated how he still had strong feelings about his ex two years into his new marriage. Now 7 years later, he is still writing his ex and asking how she is doing.
My intuition or "gut" tell me that this husband continues to have deep feelings, as well as probably has a bad case of the "what ifs" . He is looking back too much, and that isn't good.
Confronting about the email may not do any good. He will probably be upset and feel violated that you looked it up and read it. He also can justify it by telling you it was nothing but a friendly inquiry. This can cause even more friction, and separation between them.