As IGN has rightly told, you would easily have guessed that Booker was Elizabeth's father, heck I knew it the moment someone said Elizabeth looked like a person called Annabel very early in the game. I realised Booker was Comstock during the scene where Booker killed him, but I never saw that ending coming, where they killed Comstock before he was "born".

The real ending after the credit meanwhile shows a reality where Comstock, who is drowned before he came to power do not exist, and it's left to the viewer to decide whether or not Booker was not separated from her daughter

But man, the original Bioshock's Rapture cameo came as a surprise, but the explanation was straight forward. Infinite is similar to Bioshock in that each character has some similarities with each other. In this case, Booker and Elizabeth is a direct copy of Jack, who in the good end of the game became the father figure of the Little Sisters. The Songbird is protecting Elizabeth, similar to Big Daddy, while Comstock is Andrew Ryan. I was even expecting Elizabeth to throw the "Would you kindly" line as an ode.

tl;dr, shit so cash, it's worth the monies

Anna is born in the no baptism timeline. But you need to remember there are countless timelines, and there might be a timeline where the is no Anna even if he rejected the Baptism. But as showed before, people that travel through tears retain the memories of other timelines, hence why he was calling out for Anna

I think Lucete had something to do with Anna/Elizabeth's power manifesting, thus indirectly, her powers to tear timeline won't appear in the baptism never occur as Lucete won't be asked to make the floating city, and won't meet her "brother" and discover the tear

err Lucete was the one that made Columbia fly. Without her there won't be any Columbia

Yes, and the reason Lucete discovered it was due to Comstock asking her, hence without Comstock, she would not have try to find a solution for floating particles