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Hello! Most info are correct but for more clarification, it was J who turned back time first (timeline 1, where LSY died). Then when J died, LSY turned back time (timeline 2).
You were right about the watch only supposed to be used one time. However, it was supposed to be unusable the 2nd time, so HYS fixed it, which allowed LSY to turn back time (however, his powers weren't enough so he got stuck there and his timeline didn't get entirely deleted, so the West Sea Rift happened)

Its been a while since i've read the novel but if i remember correctly:
1: Sayoung turned back time the first time because J died and they wanted a second chance.
2: Then in the second round Sayoung died and J turned back time because he also couldn't accept the death.
3: The watch is what turns back time and it is supposed to only be able to work once. I think the watch was the original focal point for the first turn-back of time. The watch ended up being powerful enough that there was enough juice to do it a second time, and because J is so powerful he used himself as the focal point.
I think the second turn back though was unstable.
The west sea rift is basically the timelines trying to 'fix' themselves and shove the apocalypse into the third round too. It's trying to merge all 3 time loops.
Please correct me if i am wrong! its been a while.