So, because of how the heptapod language works, how basically the start of a sentence is constructed simultaniously with the end of a sentence (as opposed to writing this, where I begin with "So," and work on from there), it basically rewires Louise's brain to be able to see the future, in what we believe are flashbacks initially, but are revealed to be flash-forwards. I'm actually okay with this. It stretches credulity, but no more so than the idea of aliens visiting in the first place. Like I said, it's far better than Interstellar, which had a convoluted plot that involved Cooper getting into the black hole, while the aliens are limited by a completely different morphology and nature of thought.
So, basically, the idea is that the aliens have to teach humanity their language, so after understanding that, they can impart a formula of sorts that'll take years to decode. Because the aliens can see into the future (or, more accurately, they see all time simultaniously*), they know that in 3000 years, they'll need humanity's help. So, the implication is that they uplift us now, in preparation for whatever we need to help them for. Okay, fine. I can roll with that. I can even buy that Louise contacting Shang and telling him his wife's dying words is enough to get him to call off his forces...sort of. It's basic pre-destination paradox, that him telling her the words and his cell in the future means that Louise can contact him in the present/past. Okay, fine. However, the whole ability to see past, present, and future all at the same time does raise some questions, such as:
-If the aliens knew a bomb would go off in the ship, why not take steps to prevent it?
-The big issue at the end is that even knowing that her daughter will die young, Louise still agrees to have a child with Ian. Now, I don't think this is the film's intent, but it does carry the suggestion that there's no such thing as free will, that Louise willingly gives herself over to fate, that her brain has become like that of a heptapod (which might explain why the heptapod who dies ends up...well, dying). That she knows what'll happen in the future, and won't do a thing to change it. This isn't an objective flaw, and I'm approaching it from a traditional, three-dimensional view, whereas the heptapods would presumably have a four dimensional view (e.g. time), but, yeah. To be honest, I don't think the film even considers this aspect, it just rolls with it. If anything, it might explain why the heptapod apparently willingly dies, that they're fatalistic by their very nature.
-Also, the atmosphere of the craft. If Louise can breathe in their atmosphere, why are they keeping themselves separate from the teams? Maybe to make it easier to communicate via written language?
*Which actually syncs up with one of Einstein's theories, that our view of time is confined to the present, whereas in reality, every second of every event is occuring all at the same time, but we can only comprehend what we perceive to be the present.