Answers:
-What is so hard to understand about "INFINITE"? Infinite is infinite. There are infinite number of similar worlds, different worlds, world's where humanity doesn't exist, worlds where Earth doesn't exist, etc. As I said, infinite is infinite.
-The coin was a thematic element, pointing out that no matter what Booker does, things always ed up the same way. There are heads and tails, but he cannot see the tails until he gets rid of the problem at its "root". It also implies that this scenario has played out many-many times from the point of view of the Luteces, as evidenced by the checkboard on Robert on his first "real" appearance in the game.
-He didn't handle it at all. That was the whole point, that he suffered severe trauma and fabricated new memories for himself to put the ones he gained through "transit" into context, often at the cost of his real memories.
-Whether Robert is from Booker's universe is not clear. I would say it's not probable, as the first usage of Lutece's machine was to get her "brother", and the second was to get Anna, so it is quite probable that they are from different worlds. As for the flux, it's because of Anna. When she got her pinky cut off by the portal, she went on existing in two different universe, which is the reason for her powers and why there are tears in Columbia: her existence weakened the boundaries between universes.
-Fink's musical tear was just an easter egg, don't think too deeply about it.
-There is no "Columbia". The name Columbia refers to the female personification of the United States used in various forms of patriotic symbolism in the 19th century, it is purely symbolical and part of the nationalistic and religious propaganda.
-The whole quantum-power thing is a non-question. No he doesn't, and it was never implied. Also, they don't really "pass through" into other words, instead Elizabeth mashes the two worlds together, and that's why people who are dead in one universe but alive in the other freak out, as they become paradoxes. Booker, on the other hand, doesn't, as his other version (Comstock) is always alive, and he survives THAT becasue his fabricated memories make him unable to recognize "himself", so he doesn't see the paradox.
-Not a real question, next.
-Actually, yes, he died there. Booker presuambly dies many, MANY times throughout the game. However, when that happens, the Luteces just take him to another universe and he continues on without realizing it. You could argue that even Elizabeth is doing the same. Whenever he goes through the "door", it means that he died in THAT universe, but then he goes on in another universe where he DOESN'T die, and so the player only perceives the succession of universes where he did survive every ordeal. It's a bit of a meta-concept.
-No, because "our" Elizabeth ceased to exist as well. Elizabeth only exists if there is Comstock. No Comstock means he didn't kidnap her, she didn't grow up in Columbia and never got her fascination with Paris or her locpicking talent. There is no Elizabeth, only Anna...
...
Unless of course there is going to be a DLC, but I doubt it.
Read more:
http://www.cracked.com/blog/5-awesome-flaws-in-new-bioshock-game_p2/#ixzz2PdaiEvI5