First, let me pour a little cold water on the discussion. At the end of the PV, the Triforce symbol on Link's hand begins to glow. Some people have interpreted this as Link obtaining the complete Triforce, but if you look closely at the moment when the glow fades, it is the Triforce of Courage that disappears last. So I believe that what Link obtains within the Great Deku Tree is still the Triforce of Courage. In the very first shot of the PV, there is also something beneath the Great Deku Tree that appears to be glowing; I suspect that it may be the Triforce of Courage within the Great Deku Tree. Of course, this does not mean I am absolutely correct.
This is probably the part that puzzled me the most because the Triforce was not fragment from the beginning of the game, it was separated when Ganondorf entered the Sacred Realm with a dark heart, so if that is footage of the beginning of the game, then that suggest a big shift to the way we came to understand the story due to the mythos passed down to us by the same game.
The interesting thing is that separation being persistent, to where when Link is sent back in time by Zelda he brings his fragment with him, so both Zelda and Ganondorf also keeps his fragment, which becomes the irony of him finding out after being apprehended right before his execution (if we're to interpret Twilight princess account by one of the sages as the same Ganondorf after Link warned young Zelda).
So, again, the Triforce being fragmented from the beginning of the game, if we're to believe that's what it represents, baffled me. I'm intrigued.
NAVI
I also subscribe to the idea that Link just couldn't go back to that childhood. I feel like it was implied that Link was waiting to finally get his own fairy and yet with everything he experienced and what he learned about himself, it just simply wasn't going to be. Both knew they had to part ways. It still felt sudden.
Personally I believe Link went search for her because she's the only one that lived everything with him. Not even Zelda could understand what he was going through. In body he was back but what he witnessed changed him and yet not a soul would know the extend of his actions. He'd be remembered in the adult timeline he left as the Hero, but on this one it was like it never happened.
So Link was shouldering a lot having to reassure himself that his memories were real while reality didn't match and having no one else. I can't begin to imagine the level of isolation such a position concedes, so I am not surprised he decided to make his secret and personal business to try to track her down. Maybe he wanted answers, maybe he wanted reassurance, I think it is good the game will never spell it out for us, but we know he felt compelled enough to leave.
For me, that the tapestry was Link's own journal sounds just as likely. As a way to release it all before his memory became muddier. I'll have to check on the depiction of Link himself and his hat.
I don't think Navi caused Link to slip into Termina. I tend to see the Happy mask salesman as the same individual in both games, so I assumed he knew the say to access the other realm through Lost Woods, just like the skull kid is revealed to recognize Link with a wording similar to what one of the skullkids used to describe him during OoT. So because of these two shared characters, I lean to believe he stumbled there because he crossed ways and accidentally go dragged all the way into the town because of the skull kid shenanigans.

