Bioshock Infinite is about Schroedinger's Cat You take a box. You put a cat in the box. You close the lid. Then Elizabeth hands you the carbine and you shoot the box. Now there are two possibilities: (a) the cat is alive, and (b) the cat is dead. Until you look inside the box to find out, you don't know which of the two universes you're in.

This isn't really what Schroedinger was trying to say, but it does explain Bioshock Infinite. Booker is the cat. He was miserable after Wounded Knee and went to a baptism for atonement. The Reverend reaches out a hand, and Booker can either (a) accept the baptism or (b) reject the baptism. In one universe, he accepts the baptism, believes himself to be absolve of sin, and becomes Father Comstock. In the other universe, he rejects the baptism, joins the Pinkertons, and gambles his way into debt. Both of these two universes have an infinite number of parallel universes.

What Elizabeth did was close the loop. She drowned Booker and prevented both universe (a) and (b) from ever existing. It's the same thing as if she had drowned Schroedinger's cat before you closed the lid. Now, it doesn't matter what happens when you shoot the box with the carbine, because the cat is dead either way.

The epilogue after the credits is open to interpretation. You can make up any answer you like. I like to believe that Elizabeth opened a tear and sent Booker back in time to give him another chance to be her father. His memories is all that remains of the game events.

Everything Slate said was true. Comstock wasn't at Wounded Knee. It wasn't until after Wounded Knee that Booker was reborn as Comstock. Slate didn't recognize that Comstock was Booker because Comstock had aged prematurely because of the Lutece machine. Comstock, now believing he had never sinned, rewrote his personal history to celebrate his crimes at Wounded Knee and the Boxer Rebellion.

Here's where the game goes from great to extraordinary. Bioshock 1 ostensibly happened in a different universe than Bioshock Infinite. When Elizabeth takes us to Rapture, she's kind of game-jumping. In one lighthouse, Jack saves the little sisters and gets the Good ending. In another, Jack harvests their Adam and gets the Evil ending.

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for the dlc there is a great video explains how the DLC lines up with the other games and how BioShock Infinite is just a connection to multiple Bioshock universes

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https://youtu.be/tSGGl9G5Jnw?t=3759 (from 1:02:39 to 1:07:38)