From the VentureBeat article it says she was given the powers after the Leutuce twins tested on her. The tearing technology was already there but they put it into Elizabeth.
That's incorrect. The female Lutece addresses this in a Voxophone:
"What makes the girl different? I suspect it has less to do with what she is, and rather more with what she is not.
A small part of her remains where she came. It would seem the universe does not like its peas mixed with its porridge."
The only experimenting that was probably done is to determine what triggers the tears. If female Lutece and male Lutece has given her the powers through testing, the Voxophone would not make sense
EDIT:
The main thing I don't wrap my head around is how Elizabeth killing Booker before the baptism is a definitive end to Columbia/Comstock. Him being killed by her is a paradox, as killing Booker there would mean she never existed, and if she never exists she can't kill him.
You've actually understood the difficult part of this. In order for Elizabeth to exist, a single Booker has to be able to accept the baptism. If a single Booker accepts the baptism, no Booker accepts the baptism, because every Booker was murdered before the choice. The probability of accepting the baptism leading to a paradox is 100%. A paradox cannot happen, ever, and thus the probability of any Booker accepting the baptism is removed. Therefore, Booker rejecting the baptism becomes a constant, because if every Booker rejects the baptism, the paradox doesn't occur.
Think of it this way: If, before the game's events, Booker always rejects the baptism, what happens? Nothing, no paradox is created so every Booker lives out their lives. The ending turns this into a certainty, it erases the probability of Booker ever accepting the baptism because that leads to the paradox where every Booker died before making it.
