THERE WILL BE UNMARKED SPOILERS IN HERE
Liz (who at one point was named Anna) is Booker’s daughter and Booker is Comstock from the past to the future to the past again, he lost his daughter and led to the creation of infinite timelines and infinite Bookers and Elisabeths. They are also protagonists/antagonists from the other *shock titles. Also the lighthouses somehow have the power to cross time and space.
The remains of Columbia that sunk to the bottom of the ocean floor may or may not be the base of Rapture. Songbird was basically a prototype Big Daddy.
Booker is a horrible parent.