That dream is from the very beginning of the game. Fi appears to Link and warns him of the coming danger, which is pretty much what happened in Zelda's dream in BotW. Zelda isn't supposed to be the one hearing Fi's voice, though, so she couldn't. Not until she awakened her goddess powers. Fi was created by Hylia, and Zelda's powers are Hylia's, so communication was possible. Zelda says with her powers drained over 100 years she can't hear Fi anymore.
Zelda said she thought the woman was a fairy or a goddess, which is a hint that it was Fi.
Well, we don't necessarily know that Zelda has the Triforce. A Triforce mark appears when she uses her powers, but the actual triforce is a solid 3D object that doesn't dwell within a person and has to be touched and a wish made upon it. The Triforce has also symbolized Zelda herself, and the series is rife with glowing Triforce marks that are not the actual Triforce.
The mirror of twilight is not in the game, and if it was that would be evidence
against Child Timeline.
It's pretty clear that Ocarina of Time occurred in this timeline. That rules out Child Timeline because the events of Ocarina of Time that are referenced in BotW never transpired, and it's definitely not Adult Timeline.
The references to twilight are incredibly vague. Although Child Timeline is the only Timeline with the only game that involves the Twilight Realm, the Interloper War would have to be before OoT and, although it never appeared in other games, the Mirror of Twilight and Twilight Realm would logically exist in all 3 timelines. So references to Twilight could be a reference to the Interloper War, a reference to an event involving Twilight in the Downfall Timeline, or just a reference to the time of day.
The artwork added to TPHD depicts the Hero of Time meeting all of those races as a child. This implies that all of those races existed back then and logically in all 3 timelines.