Yes. RJ did stuff like that all the time. People notice different things in their PoV chapters. Perrin & Nynaeve note details about nature that Elayne does not, and Perrin and Rand give different clothing descriptions. Perrin goes into lots of detail on Faile's & Berelain's clothing, but no one else. Rand notices clothing details that pertain to status or rank, as an indicator of political mentality. It is a plausible explanation that the phenomena of Traveling aren't worth mentioning in LTT's stream of consciousness. Many times in the series, characters enter or leave rooms and buildings giving no description of the door they use, or their passage through it. It also doesn't say he DIDN'T pass through a gateway, so it is just as plausible that he did. Your interpretation is a valid one, but it is simply an interpretation, and not objective fact.
And? Your point being? This was NOT Traveling. He went to Tarwin's Gap by some other method. Remember, he was in the Green Man's place when he confronted Aginor, and you reach that by teleportation. The Green Man says as much when he tells them that, contrary to what visitors claim, his place does not move, that people come to it based on their need, much in the same way Nynaeve and Elayne found the Bowl of the Winds in T'A'R.
Never heard that one before.
I'm not sure what you mean. The descriptions of Traveling came after people had figured it out, the first instances of which were in Rand's PoV, after he had been taught by a Forsaken. Once he reintroduced Traveling to the world, people knew what it was, and described it accordingly.
I was thinking of that quote myself. It SAID that overpopulation was not a problem, because they had other means of taking care of it. And too, the BWB is written in the style of the Third Age person, looking from the point of view of an educated wetlander around the year 999. To such a person, colonization would not have mattered. Meanwhile, Moghedian revealed that the AoL was totally aware of other planets. I don't see how that matters to the Traveling debate, because there is absolutely no word one way or another whether Traveling as teleportation would be more or less viable a method of interplanetary travel.

There was an extensive argument years ago on the WoT MB, where someone (Tor, maybe? ) kept insisting it was absolutely implausible that no one managed to pass on the weave through the Breaking.

Not without a demonstration. Rand couldn't learn because Asmodean could not form the weave. Any weave is easy to duplicate once seen, if you have the appropriate proficiencies and Talents. But no one figures it out on their own, except Aviendha, and she is never able to replicate the feat. She is forced to use the different weave Egwene learned, which does not work as well for her.

But the described mechanism is not intuitively obvious. It WOULD have been an obvious one if you moved yourself, as in the hypothetical original version of Traveling, but not in what is shown. People who want to be somewhere else do not think of boring holes between the Pattern, or merging two points in the Pattern into the same place, they think of their bodies being whisked away.
But as Rand notes, it is a counter-intuitive prerequisite.

So what? Saving a group of people lacks the fundamental and visceral imperative of self-preservation. And it's unlikely that it would have been all that effective, since during a world-wide catastrophe, there would have been no obvious safe place. The Aiel went looking for one and never really found anything until the world stopped changing.
See, that horrible grammar and spelling is what led to confusion about the "bog standard" expression. For all I knew, it was intended to be something else.

Anyway, that just goes back to the implausibility to teleportation - it works as a much more plausible thing in those circumstances, because it IS intuitively obvious, instinctive and self-preserving. THAT form would have been much less likely to be lost, while the method as shown in the books is much more believable as something that would get lost. Traveling would not have made a huge difference, because the destruction and slaughter was random and unpredictable. What's to keep your places of refuge from suddenly getting turned inside out because a mad man 100 miles away flattened a mountain range, or created a new ocean? The geography of the Waste suggests that the eventual refuge of the Jenn Aiel, Rhuidean, was at the bottom of the sea when they set off on their trek. It turned out that Dragonmount & the isle where Tar Valon would be built made it through the whole thing intact, but who could have predicted that in the aftermath of LTT's death? And maybe it went through different climates too, before returning to relatively temperate once the world got back into normal cycles. Recall that at the time the Aiel crossed the Dragonwall, Cairhien was a desert.