The argument about God's order for the animal kingdom does not apply. As you yourself mentioned, there was no intercourse involved with Mary. I do believe that there was intercourse in Genesis 6. It simply states that we sin and Jesus did not. Our nature is what makes up who we are.
Sin is disobedience.
As I said before, I am not in a position to explain how this happened, since our knowledge of the angelic realm is so limited. But based upon exegesis and standard hermeneutical principals, I understand the passage to be refering to angels. And as I state in the article, Jude 6 and 7 seem to state very clearly that then angels in Tartarus are there because they committed sexual immorailty.