The reasons you have given simply do not show that Paul believed in a virgin birth. Again, he states quite clearly that Jesus was born according to the flesh. This suggests that opposite of a virgin birth.
And really, there is no reason for the idea. The Gospels never really deal with it except in the context of the birth stories. John doesn't need it, as he claims that Jesus is something quite different. Mark never needs it, and never mentions anything of the like. And considering that one did not have to have a virgin birth to be considered the Son of God, there is little reason to assume that it was necessary to the story.
As for Paul, we can't assume he believed such an idea because he never states it, and never suggests it. When talking about Jesus being born, he never mentions anything miraculous. Instead, he explains it very simply. He was born according to the law. He was born to a woman. He was born of the flesh. There is nothing in those that suggest a miraculous birth.
The clincher really is that Paul did believe that Jesus was the Son of God. And mentioning a virgin birth would have been a great argument to defend that idea, and in fact, he had the perfect places to mention it. Yet, he never does. Because of that, we can't assume he believed in it.
Really though, there is no reason to believe that Paul did believe such an idea. To believe that God impregnated a woman, in the same manner that pagan gods were said to have consorted with earthly women, would not have been a Jewish idea.