Accordingly, why did the Luteces help Comstock?
Initially, the Luteces were working for Comstock. They devised the plan to take Booker's daughter through another reality, under the pretence that he was 'selling' her to wipe away his gambling debts.
Similarly, why did Elizabeth drown Booker? Her goal when drowning Booker was to end Comstock's existence, not Booker's. By drowning Booker, she prevented the creation of Comstock in any universes, and thus eliminated any universes with Comstock in them. This allows for the cutscene at the end in which Booker still has Anna in his possession.
Simply so, why did Booker become Comstock?
He turned to Preacher Witting for baptism, so that he may be reborn as a different man and start anew, free of his past atrocities. In one reality, Booker was unable to go through with the baptism, while in another he accepted it, and took on the name Zachary Hale Comstock.
Are the Lutece twins dead?
Well, they are alive throughout the game because their sabotaged machine didn't kill them; it scattered them across time and space. Since every Comstock died, there was nobody to fund the Luteces' research and sabotage their machine.