Time is dealt with precisely and mathematically in Relativity physics. Time is not absolute in the Newtonian sense we all experience intuitively. It moves at a different pace for different observers. But the only way you can alter the rate at which you move through time is to subject yourself to acceleration or gravitation. Events whose separation is "space-like" cannot communicate with each other and events whose separation is "time-like" can communicate only in one direction. You cannot see the future because that would involve communicating in the wrong direction. (Which is a Relativistic way of saying that you cannot see the future because it has not happened yet. You cannot see the future because the future does not exist. "Future" is an abstract concept we use to refer to regions of time that do not yet exist.) And I repeat that being able to see the future because you learned a special language is as loony as Scientology.
Right. And, I think that's my point. Relativity is entirely deterministic, no? So, if we had access to all the information available, and all the laws of physics, we could map out the future. From the right perspective, time and space are one 4-dimensional object; if you could observe it from that perspective, like the "bulk space" in 'Interstellar,' time would be much like another spatial dimension. And free will, of course, ends up playing a part in the story.
I didn't interpret Louise's fugue states as "communication," so much as I interpreted them as temporarily experiencing time in the same way the Heptapods do -- non-linearly. She was remembering her future, in the same way you and I remember the past. But communication wasn't really occurring -- at least, not in a way significantly different from when I remember what I had for lunch yesterday.
I don't think learning a language could ever make you experience reality this way; I'm not sure any
biological organism could ever experience reality this way. But I also don't believe magic space rectangles can make monkeys smarter or give people superpowers, or that we could ever break the laws of physics as we know them, to travel faster than light, or that laser swords exist, or . . .
I don't think it's fair to single this movie out, when it at least bases its speculation on nature as we currently understand it. Linguistic determinism is a thing, though not to the extent depicted in the movie. And the laws of our universe -- at least, the macroscopic ones -- appear to be deterministic. I'm not saying this movie's necessarily for you, but . . . you seem awfully determined to neither see nor like it. I mean, comparing it to Scientology?!? I'm not sure any greater insult could have been levelled!
Edited: for spoiler-y stuff!