It was the scene where she was alone with the heptapod in the pod btw.

In a universe like this, where time can be perceived as a circle, where you can at will look into the future/past..
Is there free will ? Or is everyone predestined to do that one thing they see ?
The movie doesn't touch probability in any way, and Louise doesn't even attempt to change what she sees. She follows the same path she saw, and there are basically 2 options here; she either decides not to change anything, because of reasons, or she is unable to. I'd assume any logical human being would do what they can to prevent the death, or at least prevent her husband leaving, maybe tell him about it earlier.. something.
Then there is a third, hidden option:is she.. still human ? Leaving theology aside, what makes us human is basically how the brain works, and that depends on a ton of factors, time perception being one of them. Would this change turn her into.. well, something else ? Her and the entire population of earth for that matter...

Wait so is only Louise capable of thinking this way too or like she said, through the language people were able to unlock that ability? So by teaching it to the rest of the world, and presumably her own family, wouldn't the daughter have known she was going to die as well? And why couldn't they have thought many different possibilities as to how to cure her, ruling out what would work and what wouldn't? I think this points to life being linear in this timeline, and in that case, there would in fact be no free will as we know it.

I think it's not only her, though it is only her story we can see.. but I assume it's something everybody can learn, and that's the reason the Chinese leader gives her his phone number and tells her the numbers - he knows, he can see it too. In fact, this in my eyes completely changes him as a character, which I also found really refreshing -from a hardline villain that would rather wage war than seem week, he.. turns out to be an intelligent ruler that sees the coming paradigm shift, so to say, a lot faster than the west.

I think this is where you can dive into the philosophy of the movie. I'm gonna pull something out of the Matrix (whatever your opinion of the movies themselves, they are quite deep in terms of a primer on contemporary philosophy) - to paraphrase, "You've already made all of your choices. Now you are here to understand them".

I always thought that was beautiful. And it makes a lot of sense for me. The linearity of time is a human perception. I think that's been well established as an accepted theory. I don't believe in an all powerful creator and fate - the world is too chaotic and too many things seem to happen by chance. Then how can humans ever make their own choices if, in reality, everything has already happened, in a sense? In any mathematical model, you can predict the outcome if you understand all the variables. When a human joins the world, they are another variable in the never ending equation of life. If enough was known about this person, we could theoretically predict everything that will occur in their lives. That person has still made all of their own choices, but because those choices are integrated into the larger scheme of life, we can predict "future" choices. I think that's how life works in general - time is not actually linear, so if we were able to see life outside of time, we could see ALL the effects of throwing a new variable in. That variable (a person in this case) has made all their own independent choices, but it has affected the system in a predictable way and with time, it would seem as if everything was "fate". That variable then experiences those occurrences linearly, making it seem like they are making these choices one after the other when in reality, they have already been made and the person is now coming to understand what those choices mean.

I think that perfectly reconciles the non-linearity of time and fate. We make our own choices, but we've already made them. Now as we go through life, we come to understand those choices and learn from them linearly. It also fits in with Arrival, as she clearly doesn't do much to change the outcome of her life. She had visions of her choices and through the course of the movie came to understand them.

I agree with this - it didn't change her brain, just the way she used it. She may have more inclination to develop this ability, but I didn't get the impression only she could do it.

They taught her how to do and she wrote a book relating to it to teach others how to tap into that part of their brains to be able to do it as well. That's the main reason that the alien species gave her the gift to be able to understand how to do that and teach others as well so that the human race can help them in the future.

I don't think learning the circular language gave others the ability. Lousie had to tell Ian about their daughter's impending death. He didn't see it on his own. And regarding Shang, he didn't have it either. He receives a call from a stranger on his personal cell phone and she utters his wife's dying words to him. It blows his mind and causes him to stand down mainly based on not fully understanding, other than it must have been something related to the Aliens. At some point later he learns about Louise's book and realizes that it was her that made the call. He then goes out of his way to meet her and impart the knowledge she would need to make things right 18 months earlier. He goes so far to tell her, "I don't understand how your mind works".

For the record, his wife's dying words were: "In war, there are no winners. Only widows."