I can definitely say that it's possible, and that I've thought on the matter quite a bit; or at least how it would be possible. Since I first met him I've been going over that conversation in the back of my mind, and I can see it giving some backing to that theory. Along with a bunch of things that I can use to expand my Guide
This is pretty crazy. I've been working on a build based on the Sole Survivor likely being a Synth, based on Golden Fool's excellent post (see his link above).
And sure enough, now we have more questions in the DLC alluding to this very possibility. I think it's still unlikely that the SS is indeed a synth. Although, you can imagine, knowing the Father let the SS out of the Cryopod, that they may have gone one step further, testing their latest creation with some new "memories," for the ultimate experiment.
Regardless, I find the possibility fascinating and am glad they've added more content to muddy/expand the water.
I also find roleplaying the SS as possibly / probably a synth one of the more intense ways to play the game. It makes you reconsider almost every decision and interaction in the wasteland.
My supposition for your 4. is that Father's last decision as director is to prove to the scientists, synths are ready for more. (though, based on how many are rebelling...he's probably wrong.)
Hmm, interesting. I always noticed some of the other Dwellers in the pods barely moving, like maybe shifting a bit. As for that, some of my characters have been synths with the Sole Survivor, who died in the pods, or out in the Commonwealth, implanted in a Synth by Father's order, like as some act of love, to try and reconnect with his father