Before I go into details remember that this feature is really a third act. We are not seing the whole story.
From my pov, JDW is chasing what he think is plutonium and he is trying to prevent a nuclear holocaust.
There is only one realm but it's like one side is going back and the other is moving forward. It's not an alternate reality. It is the same reality but not moving in the same direction. Hence Pattinson's hands gesture.
Sator is your typical foe. he is trying to control the world and bend it to its will. When the URSS fell, he discovered a box connecting him to the people ahead of time. He started working with them as he was making his fortune as a weapons' smuggler and plutonium dealer.
The world is devastated by water flooding. An ecological disaster. Not a proper war. The idea for the people ahead of time, is to use the algorythm to reverse the entropy of time. It is not to nuke us. It is to simply erase us by going backward in time. Explained in the feature, time is constantly fighting back and forth. JDW states that he thought the grey boxes were plutonium but it ain't. It is the algorythm.
The problem is that the Russian wants to be god like. He wants to be ALpha and Omega (beginning and end). So he connects the delivery of the algorythm to his own death which is ticking bomb (considering he only has few months to live). If the Russian dies when the algorythm is delivered to the people ahead, it is a signal for them to start reversing the entropy of time on a global scale. It is a warranty. It also a safe net for the Russian as he is unkileable.
Think about the feature as a representation of the magical square Sator-Arepo-Tenet-Opera-Rotas... That would explain the feature: You reap what you sow.
Regarding Poesy' sentence about the upcoming conflict: you can it "both ways", it's either we are getting stuff from our own past or the remnants are from Stalsk 12 (battle at the end of the movie)
The algorythm was created by a scientist (a female one) but the scientist knew other people would use for destruction. So she decided to send it back to us so that it was practically unreachable. What I think we are missing is that Poesy might be the scientist in question. She just does not know it yet. Throughout the feature no one is capable of explaining this phenomenon. It is there, we can see it and experience it but can't explain it for now. Very much like a black hole. We can observe a black hole but we can't say what it is because we can't explain it. Only make hypothesis. To go further I think, either JDW or Pattinson (or both) will be the one hiding the algorythm (as seen at the end).
Supposedly, JDW is working this operation for a long long time. He was after plutonimum. he was trying to prevent the wrong person having nuclear capabilities. On this mission, he hired Neil from way back and they go a long way. If the feature had a STANDARD beginning, we would have more background story for them two. Pattinson knows a lot about him (no alcohol on the job).
Explained in the feature "TENET" can open the right or the wrong doors from a social perspective but also as an experience. When you enter one of those vaults/turnstile, you have doors. At the end, when Pattinson use his own turnstile, we do not see him go through both doors back and forth, we only see the reflexion of him going through one of them. Considering he is moving back (blue team) and he enters to move forth, his action means he has no future.
-JDW kills her because she lied to him. Tried to keep him on a leash will not providing every answers. Also considering JDW has a crush for debicki and the indian woman wants to kill debicki it seems clear. Understand that Debicki and JDW already know each other and already have an affair, they just don't know it yet. Stop thinking linearly as ATJ said it
-I think it happens either at the same time or right after it. When he eats the pils and finds himself locked in a wind turbine.
-For the wounds, I would suggest you to imagine a bullet shattered in your body that would get back to it's original form and then wind back up into the canon of the gun. That idea, to me, seems painful af. when JDW stabs himself then after they go into the turnstile, after the car crash and when they are on the boat the injury appears So you go through pain from less intense to more intense.