It's a time traveling mutiverse story which is worse. Why would the first Comstock open a dimensional gate in the first place? Who found the scientists Lutece? Why did they open the dimensional portal the "first" time? To cross over the multiple dimensions someone had to do it "first".
Comstock did all of that because of Lutece's expertise. He met Lutece who was a scientist. She created all the technology that allowed for the floating city and tears to exist.
That said, because of the radiation, Comstock got cancer and became sterile, but he wanted a child as an heir to keep his vision a reality and to keep his religious society subdued. Lutece opened a hole to another existence where Booker never got baptised and had a baby. In that process, Lutece met her male doppelgänger and brought all 3 through: Comstock + baby + male Lutece.
Now because of Lutece's technology, they were able to even rip tears through time and space to steal other technologies from other points in time and also even entertainment. Which is why you'll see modern songs being sung on the record players but in old-timey styles. There's a red tear in the game explaining this too.
Comstock also wanted to take over America. So he brainwashed and manipulated a populace and used future technology to create an army to destroy the people below and take over. In that process, he killed Lutece because he didn't have a need for her anymore.
But a female and male Lutece that are outside of the timeline keep replaying the same timeline over and over trying different things to see if they can get a different outcome. They may seem insane, but they do feel responsible for the horrible events that take place. In the ending, they describe Booker as their 'hairshirt' which means their item of atonement.
It's unclear how Elizabeth got her powers, but I imagine Lutece helped her become that way through experimentation or because her body got caught within a wormhole, her conscious was fragmented and she had a bizarre understanding of the universe. Lutece did however create the technology to keep her powers subdued and even drain them over time to help Comstock. That's what the tower is for, it drains her powers. Once the tower is destroyed, all the understanding of the universe comes rushing back to her.
As for Comstock dying, in the ending, Elizabeth states she sees all doors (all possibility spaces) and in only one of them does she see a chance to kill Comstock. She then goes on to state that, "It will only be over when he never even lived in the first place."
So with her ultimate understanding, she takes Booker to a place where they root out all possibilities of Comstock, all possibilities of Elizabeth and all possibilities of the Luteces destroying the world through enabling Comstock. That's not to say Lutece doesn't ever find her male counterpart again in the remaining timelines, but that's neither here nor there.
