the Chinese general knew about the phone call at the same time as her.
She was simply "remembering the future."
The Chinese General knew about the phone call from the time he got called, which was a number of months before Louise met him at the party in the flash forward. In Louise's present she was still coming to grips with her ability to see the future, so she struggled to remember the future and remembered her conversation with the general at that party in the future.
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The language itself was what was giving her the ability to see through time. As soon as she started studying it, she started getting glimpses of the future.
Why Ian and the other scientists didnt get the ability is probably just because they weren't as good at language study.
But how did she get fluid understanding of the language after the rogues tried to blow up the ship - was the ability to access the weapon/gift and if so, why didn't the aliens do a conscious transfer to her before all the events leading up to it -- they obviously had the ability and would know what would happen.
I think this is a misconception, I think it was clear her understanding of the language required her specific knowledge of language and her study of the language, they couldn't simply beam the language into her brain.
How did she know that Hannah was going to die before the events the led to aliens revealing to her the time loop capability? Did she end up telling Ian or did she alter that time and if so, would the alien scenario happen again? Did she always have the ability --if so, how come she didn't tap into the oncoming events -- if she didn't have the ability before hand, why did Ian leave the marriage?
Hannah dying is likely the saddest, most emotional event of her life, therefore its probably the thing she remembers most easily, along with Hannah's life. It was the first thing she started "remembering" when she started remembering the future.
Like how an amnesiac doesn't remember everything from their past at once, Louise didn't remember everything from her future at once. At first she didn't even know she was remembering the future, she had no clue the Hannah was a real person until she had the face to face conversation with the Heptapod.