Forum:Connection between Infinite and its DLC

WARNING: SPOILERS BELOW

I just played through the whole series but there are some points I can't understand.

- First, at the end of Infinite, Elizabeths drown Booker to death before he can make the choice whether to accept the baptism or not, resulting in preventing Comstock and Elizabeth from existing. It means that there are no multi-dimensional Elizabeth created by being brought through the Luteces' Tear and got a part of her body separated. So in the BaS ep1, how can that Elizabeth still exists when Booker has been drowned?

- Second, in the middle of BaS ep2, we can see Booker and Elizabeth in an elevator in Columbia from the perspective of Elizabeth. What I want to ask is, are the Elizabeth in BaS ep2 and the Elizabeth in the main game the same character? This troubles my mind so much.

I really appreciate if anyone can clear that up for me.

P/s : I'm not a native speaker so if you find it hard to understand my questions, I will try to make it clear for you. Thank you.