As much as I'm a great fan of logic and naturalistic views, I don't think you can apply logic and scientific, physical facts to God, because God is supernatural in nature (most Gods, anyway). The logic you use in this thread is logic that works well in the material, observable, testable universe. But no matter what scientific facts you may come up with, or what sharp logic, you will only get a point here and there in the conversation with a believer. The Joker in the deck will always be "God did it that way and God can do anything". Virgin birth? Not a problem at all for God, the creator of everything. Feed 5000 with a small amount of food? Not a problem for God (although as you mentioned, he probably had to 'beam' it over from somewhere else, since he was done creating). Walking on water, making water into vine? Not a problem for God. Healing the sick? Not a problem.
Completely illogical for a human being to be able to do any of these things, but not a God, because he is supernatural (outside of the natural laws). God - if he exists - may not be able to make 1+1=3, but he could influence your mind into thinking it makes sense that 1+1=3. He could manipulate the natural laws. So you can't really use logic to attack those miracle examples directly. You have to start from the bottom up, so to speak. For instance, you may show a Bible believer that the Bible can't possibly be the infallible word of God. But - backed severely enough into a corner, a Bible believer may eventually agree to say that the Bible isn't infallible, and isn't as directly inspired by God as previously thought. So what you're left with in the end then is a believer with a very general belief in the God of the Bible, and a belief that God's thoughts are still found there (somewhere between the lines).
And then you're back to using logic against something supernatural again. If people choose to believe in God for no other reason in the end than that they want to, you can't do much to change their mind by using logic.
But, if you get to a point where the person no longer believes in the Bible (or any other religious text defining God), but simply in a 'some-mysterious-force-out-there' God, then you could start applying logic again to explain how it's weird how God has done things the way he has throughout mankind's history (hmm... I feel like I'm conducting a reverse Bible study here...).
But you could still get stuck with "I'm sure God has his reasons that I have no way of understanding - who am I to judge God?".
So logic and physical evidence can take you so far, but it will eventually still be up to the individual person if he/she is willing to use that in order to stop believing in God, or apply faith (which is more like a gut feeling) and keep believing no matter what - maybe simply caused by an experience that to that person was very real. That experience could perhaps be explained away too - but they choose to apply faith (the "gut feeling"), and see it as evidence (to them) of a supernatural presence.
And they should have that right - even if I personally may think they'd be wrong. Kinda like I would advocate the right to free speech, even though I might disagree with the statements some people make when they exercise that right.