Okay, finished, and I've got a lot of ground to cover.
The Markings on Booker DeWitt's hand: The obvious answer is Anna DeWitt - but we're never told by Booker himself what the markings mean. Before the reveal, I was fairly certain the AD stood for "Alternate Dimension." Which makes sense since, in almost the entire game, you are not in your world. You die several times in the game, namely in the introduction during the baptism and in the few encounters with the Songbird, and each time you are revived in a "dreamworld" (which is in fact the dimension you came from) you open the door - thereby opening another dimension where you live.
Furthermore, the logic of the game suggests that you can only die in the dimension you came from - which explains why in the end game you have to go back to before Comstock's baptism (thereby killing both DeWitt and Comstock), and also explains why people become disoriented and bleed from the nose when they're in a different dimension. They can SENSE their own death. Kind of freaky.
As far as parallel universes, you can see plenty of references to it in the game. There are several NPCs in the world that come in pairs, and beyond that it seems every character has its foil. Anna DeWitt is the same as Elizabeth. Booker DeWitt is the same as Comstock. Booker's dead wife is the same as Comstock's dead wife (appropriately, both died because of the child).
I can see how Booker's atonement gave way to racism. He forgave his sins at Wounded Knee by playing up the importance of the battle through racial superiority. It's worth considering that at the time it wasn't even an especially unpopular opinion to have...and those that have suggested Mormonism was the inspiration seem to be pretty on point.
And, finally, the game explains game theory (one of OP's mains criticisms with the game), and it's game mechanics through this parallelism. Vigors may not have as close of narrative tie for their inclusion...until the end, when you learn that all of our universes are tied in interrelatable in idiosyncratic ways. That alone makes the ties to Bioshock so much more palatable. I feel bad for the people in the Bioshock Infinite thread who are going in having not played Bioshock 1, because...even though it may not seem that big of a deal, it's a huge part of appreciating the game's intricacies.
Elizabeth is similar to the little sisters. An integral part of the world's structure, guarded by a giant that can both be amicable and sinister. The Songbird and the Big Daddies both have glowing eyes that indicate their level of friendship, are related to animals from their world (Daddies are based on whales, Songbirds on...birds). "Circus of Values" are in there. At one point, Liz crawls into a vent. The Letuces' talk about two sides of a same coin...and this seems to be a literal realization of that analogy.
The final parallel is real life. Bryce Dewitt is a physicist.
http://en.wikipedia.org/wiki/Bryce_DeWitt
Anthony Comstock is a Victorian moralist who preached cleanliness of character while ignoring the seedy underside of life.
http://en.wikipedia.org/wiki/Anthony_Comstock
Sorry for the disjointed post. Had to get it out.
I always read spoilers ahead of time, to me it makes the games better.
Gross.