Totally agree here. I think Mat and Perrin are very special souls and spun out of the pattern as needed and can't be bound to the horn. (Perhaps similar to the Dragon)

2-3 more books

Her being present when the Bore is made is so interesting. She was still a researcher at that point, and while scorned by Lews, wasn't evil yet. Could she have been affected by the dark one in that moment?

Good point about the true power. And I agree, Demandred is pretty much out of his mind the whole time, so we can't apply logic to the duels.

I like Alanna. She deserved a better death than she got

Her story is definitely the most tragic of the main cast. She has become one of my favorites after re-reading the series. I've always thought of Egwene as the female counterpart to the Dragon. Loial's quote about Rand kinda fits her too "he came like like the wind, like the wind he touched everything, and like the wind he was gone".

Most times the lore discussion goes deeper than the author intended. It's one of the things that makes this sort of story enjoyable. That being said, don't kill the verisimilitude

I think most ages take place without channeling. In my head canon, fewer and fewer channelers are born and the ability fades away until the pattern requires it in another age

The city was built by the Aiel who continued to follow the Way of the Leaf. At some point towards the end of their journey, they were joined by Aes Sedai who guided them. One of these Aes Sedai is present when the first of the Aiel come to make the pact to go through the columns. Presumably they are given instructions to enter only once. Aiel generally do what Aes Sedai tell them and also, many die just entering the columns, so that would serve as a pretty good warning to follow the directions. In the instance someone does go through twice and gains knowledge of the future, they likely are driven mad. As far as why the city and items of the power end up where they do. Ancient Aes Sedai had a far greater knowledge of prophecy and probably knew how certain things needed to/would happen. They made the prophecy of the Dragon during the Breaking, as well as making Callendor and the Eye of the World, and stashing the Horn in the care of the only creature capable of safeguarding it until it was needed. They sent the Aiel on their journey to protect the Aiel and the items in their care. It also gave them purpose and ensured their people would survive the breaking.