This is true, but if Booker dies, and that does in fact stop all bookers from existing past Wounded Knee, there's no way for the post-credits scene to exist as we know it. The paradox discussion allows for both.
Right, but if Liz does kill you before the choice occurs, this only happens because Booker was given the choice. If he's not allowed to make the choice due to Liz killing him, it's impossible for Liz to exist to kill him in the first place.
Essentially correct. Elizabeth only exists if the baptism event occurs as a choice, since this will split off into Booker and Comstock. But if she kills Booker before the choice is ever made to become Comstock, it's impossible for her to have killed Booker in the first place, because negating the choice also negates her ever existing as Elizabeth because Comstock never took her, and she never then generated any tear abilities.