Ok this might become a thread in which I ramble on mainly to myself, but I have to get a few things out of my system I guess.
About the teaser trailer #1:
More knowledgeable people than me have done their analysis videos and stuff about it, but here are my thoughts:
The first scene immediately made me laugh. Throwing people into water is a well-known thing in the books (such as when Lan once threw Moiraine into a pond)
And that is so typical for Nynaeve. I don't remember her doing it to Egwene in the books, but we know that both Wilders and Aes Sedai use sometimes... creative ways to get women to channel. The scene is ironic since Nynaeve herself has some problems with that in the books. I wonder if the show will do that similarly, or if perhaps Egwene is the one with the problems?
Her saying "Be Strong" reminds me a bit of the words spoken during the Accepted test. "Be steadfast" (IIRC). Perhaps foreshadowing.
Anyway. The Two Rivers and Winespring Inn look nice.
I am not sure who the crying man is. He holds a serpent ring it seems (although those look different. Less a simple ring like in the books but they seem to have gems that show the Ajah color?) so I agree with others that he might be a Warder who lost his Aes Sedai. That also explains his seemingly reckless fighting style.
I am pretty sure that Egwene coming out of that pool is the Novice/Accepted ritual, with the Ajay colors on the water.
Tar Valon looks awesome IMO. I see people critisize the White Tower, but from the descriptions in the books it looks pretty accurate apart from the fact that it isn't smooth enough. Ogier buildings usually look seamless.
The rest of the city looks pretty similar to what we know from the books (albeit a tad smaller). I might even have spotted the Grove in one of the shots but I might be wrong.
The Hall looks good, Leane (here and in a later shot) looks grumpy and has her staff, as she should.
I've already commented on Siuan, overall I don't mind her I guess, if the behaviour fits.
A Green sister heals Moiraine, possibly Alanna?
We see strands of the One Power in Emondsfield. Not sure what happens there.
Red sisters!
Rand shoots a bow but he has a slightly weird drawing technique and the bow looks a bit short and thin for a Two Rivers Longbow.
Matt, possibly in Shadar Logoth, with the Dagger.
Mashadar. This is definitely Shadar Logoth.
Is that... Hopper?
I am not sure what Egwene and Rand are doing there, but that might cause some braids getting tugged and/or ears getting boxed. Might be in the bath in Shienar? Anyway, they seem a bit closer than in the books, possibly because the characters are also older in the show.
Next we see Tam and what I think is a burial, probably for Aes Sedai killed by Logain.
The Hall again, and then Lan, Trollocs, Logain, Nynaeve in a misty forest, more Aes Sedai and some action with Aes Sedai and Warders.
Also horses! Namely Aldieb, Mandarb, and a few more of which one might be the mighty Bela.
The stone thing on the hill is a Waygate I think. And GAH Rand carries a bow (strung it seems! Not good) on his back... and it is too short.
Last we see a Myrddraal, and Moiraine channeling Saidar.
I wonder if we will see One Power wielders without visible strands (POV of someone who cannot feel the Source), or strands that are different because of the different elements.
I already see people complaining that it looks a bit like in Avatar: The Last Airbender but in defense of the producers here: It looks cool and Robert Jordan's descriptions of how using the One Power works/looks like predate ATLA by 15 years.
It deviates from the books a bit though. IIRC most Aes Sedai don't do exaggerated movements while channeling the Power. That goes so far that non-channelers don't even notice that they are doing something, they might just notice that the Aes Sedai look focused or straining.
But yeah, style points. Perhaps they will use the motionless channeling to give an extra cool impression when they show the really strong wielders such as the Forsaken, Cadsuane or Damane.