So the choices you make don't affect the story (and really with a story this complex how could they) mostly they are there to tie you emotionally into the game.
For example I didn't throw the ball at the couple, and when i bumped into them later I was actually happy to see i had helped them escape. That's probably under five minutes of screen time, but I was genuinely involved regardless which is impressive.
As for 'liz powers origin i didn't see an in debt discussion about it and was wondering on your guys theories?
My leading one so far:
There is the voxophone early in the game referencing 'a part of her in the other world' I took this to be a reference to her severed finger. With part of her physically in the other world the tear could never fully close., and she learned how to open it. Given enough time She expanded this power to what we see in the game.
As for the multiple universes, i'm inclined to agree with blue slightly, given there are multiple universes it seems likely that in some of them Booker fails.
It's true that by drowning at the end we solve many of the ties to constad, but while there are a lot of liz's at that final scene, there are not really a lot compared to the number of worlds we now know exist. So yes there are world in which we failed, or columbia never existed.
This in turn is what I took the visit to rapture to mean, while the fact it was rapture was obviously a tip to us as fans, the timeline itself suggests a world where similar choices were made (as vulc points out the bones of story are very similar) but the choice was mad to run to the ocean not to the sky (this could mean in that world the lutrecs failed, and the balloon technology wasnt invented Hence no tears).
It's also worth noting that we have no way of knowing which universe we actually saved. When we are taken to see old 'liz she is wearing the brooch we picked on the beach (coincidentally i chose the bird). The liz we then rescue and finish the game with is not seen to be wearing it (at least that i saw).
To my mind this would suggest that we are sent back in time and shifted universes again by old liz. So the New York that this booker comes from presumably has been destroyed.
All of that said (and I must apologize for the waffle but it is very hard not to rant about this game once i start) is that the multiple universes are not the point. The story is about Booker and Liz. In at least one of these universes you did win, you did save them and it did work out.