Thank you AH. Your obsessive attention to details is much appreciated.
As I recently rewatched this I was also confused on the point of her survival after Doom disappears. In an early episode she was reviewing and writing the contract details and she says that either way she dies or regardless the person she loves will die whether she chooses doom or not from which I concluded she would die regardless whether the person she loved the most died. However, as episodes roll out there are many contradictions to this idea in particular her focus on Doom's dying and their dialogue about her continuing to live on etc.
Your analysis also makes sense out of God's comments/warning to Doom that Tak might select the end of the world to keep Doom alive, and Doom's subsequent comments to Tak while they were standing in a world without people that he would become nothing or nothing more than a speck of dust floating about if he was left in their world without people. He was reassuring her that her only real choice was to end him because in ending the world he would disappear anyways.
My understanding is that once Doom disappears then God would birth a new Doom to replace him. As interesting as it might be to see the new Doom's reaction to appearing in a world and pondering what happened to his predecessor in the job it wasn't important to the core story.
As for comments that the second plot with the love triangle was unnecessary I disagree. The three of them fumbled around for 10 years trying to work out who loved whom. This is in strong contrast to the passion lit and burning hot in a mere 100 days of our main couple. This reminded me of a couple I read about it an history book on certain events in the 1800's in the US Old West. An outlaw stopped by a ranch and was invited to dinner. He met the 16 year old daughter of the farmer over dinner and when he left she left with him. Their devotion to each other was intense and well known back then and over the next 10+ years they committed many crimes together until a large posse cornered them and their gang in a remote house where they refused to surrender and died together - an earlier Bonnie and Clyde.
It's common that the time it takes to do something is a function of how much time is available. How many to-do lists written on a weekday get finished on the weekend? Tak had 100 days whereas Ji Na had unlimited time. The screenwriter put the following comment in the dialogue more than once - “All humans’ days are numbered. They only live forever until they realize it.” Tak's realization her days are numbered and Ji Na's not realizing that her own days are numbered is the contrast highlighted, and further Ji Na and Ju Ik were perhaps themselves goaded into acting only after they were forced to realize their own mortality by learning of Tak's imminent end.