Wow! Thanks for replying. This reply is excellent and very skillfully written. However, I will point out that my timeline starts on the spot of OTL Juneau, on the Alexander Archipelago, which provides a lot of experience for the Tlingit tribes to get used to marine traveling.
Plus, the Alexander Archipelago is close to the Haida tribe, who were well known to raid as far down as California (I think).
I'd say the big skill necessary to develop is open ocean navigation, since hugging the coast as the Tlingit often did means slower travel times. Regular trade across open ocean to an island like Kodiak would help those skills evolve.
The Haida raids did not occur until the 19th century when they had guns and the people in northern California did not (and these were very rare events). In precolonial times they didn't travel much past Vancouver Island. That's not to say the Pacific Northwest was a peaceful place since the oldest evidence of fortifications goes back 2,500 years IIRC and there's several 1,000+ year old archaeological sites that correspond with oral histories regarding battles and massacres, but there wasn't as much long distance raiding or trading.
If the Haida gain the outrigger canoe, and all the other naval technologies, then in my opinion they would be intergrated into the newly made Pacific Northwest trade routes, and spread those trade routes all over the West Coast of America and maybe even inland (you can share your opinion on what the Haida would do).
Probably. But I wouldn't say inland since "Haida" is more just a linguistic grouping than anything. Haida, Tlingit, and Coast Tsimshian societies all shared so many common elements which based on oral record seem to have evolved together and extensively borrowed from each other that language is the easiest way to say where one society began and the other ended. So Haida expanding inland would mean they'd have to marry into Tsimshian groups and would end up speaking Tsimshian (especially since IIRC all three cultures are matrilineal).
Regarding NorthEast Asia, is it possible for the Tlingit traders and merchants to go even farther than Kamakatcha and the north part of the Kuril Islands?
It is possible, but would not amount to much for the reasons I said--there already is a pre-existing trade network there in which the people involved possess similar, if not superior, technology. The Ainu and Nivkh have centuries of experience as middlemen, and would not want to turn over that role to newcomers. There is also going to be a limited market for whatever goods the Tlingit could get from it because the Alaskan coast is very rugged and can only support a given number of people. Using the relevant example of medieval Norway with its similar climate and environment, that can't be much more than 500,000 at most from the southernmost corner of the modern state to Attu Island (and in many areas would be very fragile since high-quality woods like yellow cedar and Sitka spruce don't grow well/at all so would need to be imported). It also really doesn't help that the Tlingit are more vulnerable to Old World diseases than the Ainu or Nivkh and I can't imagine spending weeks and weeks sailing very cold seas rowing a boat and messing with the sails does anything good for your immune system.
That's part of why I favour southern Kamchatka for this sort of trans-oceanic trade route, since it would be akin to the role the city-states of the Malay Peninsula played in the Indian Ocean trading network. Although there's obviously differences since unlike in Malaysia where strong states like the Khmer or Chola or Javanese states were actively involved in manipulating it, there's no local hegemon since Japan and China are too far away and the population density is too low. Now yes, large communities of Persians and Arabs did establish themselves in China, but that may be due to there not being enough Chinese overseas trade to account for the huge demand in both China and the Middle East (two incredibly wealthy regions with a huge population) so Arabs and Persians complemented those roles. That might be the longest medieval trade route by distance, and I do admit there's probably factors I'm not aware of involved. I'm just not sure it's plausible to have those factors in this scenario, even with some insane West Coast Indian alt-agriculture wank where they have an equivalent level of economic development and depth of time as the Old World.
Given that the Ainu have lived in the Kuril Islands and a part of southern Kamakatcha, it could be possible for the Tlingit traders and merchants to learn to speak the language of the Ainu reasonably well, and learn of the rest of the Kuril Islands, Sakhalin, and maybe even Hokkaido and Manchuria?
That was actually not true until the 14th century since the northern coast of Hokkaido and the Kurils were inhabited by Nivkh speaking people of the Ohkotsk culture. They may have been the first group called "Kurumisu" (which seems to just be an Ainu term referring to people on distant islands). They seem to have died out because the medieval Ainu were very expansionistic, probably related to both immigration from Honshu and in attempts to secure the valuable trade between China and Japan (and to a degree Korea plus the Jurchens and other Tungusic peoples). The ones in the northern Kurils (their last holdout) seem to have greatly declined in the 14th century, probably as a result of epidemics caused by increased trade which undermined their ability to sustain themselves and meant by 1500 or so they were assimilated by the Ainu (but still distinct enough that the earliest European explorers commented how the natives of the northern Kurils were different in appearance than the southern Kurils). The specific culture you're speaking of did not emerge until around 1600.
This could lead to the Tlingit traders and merchants leading trade expeditions to those areas, which in turn could lead to further trade contact with Asia, which could possibly have interesting effects down the road, especially if the Mongol empire shows up and/or Japan turns a interest to the islands of the Ainu (Sakhalin, the Kuril Islands, and Hokkaido).
The Mongols did invade Sakhalin OTL to protect their Nivkh vassals. It was a very lengthy campaign mostly involving said Nivkh vassals supported by a few ethnic Mongols and Jurchens, but successful. They even built a small fort at Cape Crillon, the southern tip of the island. If there was a source of valuable goods like ivory coming from further northwest, they'd probably just add it to the tribute the Nivkh were required to send them.
On the other hand, it would support the idea of a two-front campaign against Japan. This doesn't seem to have ever been proposed and likely only existed in the imagination of Japan's elite--the Mongol attack on Sakhalin probably contributed to a series of Ainu uprisings in northernmost Tokoku that lasted sixty years by disrupting their trade and denying an outlet for expansion, and this was interpreted by some as a sign of impending disaster and war with the Mongols. The logistical preparations for the campaign and securing Hokkaido (probably with the aid of the aforementioned Okhotsk culture Nivkh) would be useful in increasing access to trade and also benefit powerful Mongol elites (Hong Dagu and his clan plus the powerful descendents of Genghis Khan's brothers).
But I'd say that even your broadest possible North American trade route is just going to be another source of goods the Mongols (or whoever rules China) already get. I can see ivory, jade, antler/deerskin, and furs being the main goods, which are valuable but nothing new--it's just an additional source. More important for developing that corner of Asia would be the logistical preparations for a two-front campaign against Japan which would involve repopulating northeastern Korea and the coast of modern Primorsky Krai (it seems to have been fairly marginal compared to a few centuries prior to the Mongol conquest) plus a greater densities of forts and farms in the Amur Basin in general.
As far as Japan is concerned, they weren't really interested in those northern lands since they already were getting everything they needed via trade and there was always a powerful local family mediating that trade like the Abe clan, the subsequent Northern Fujiwara clan, the Kamakura/Muromachi era Andou clan, and lastly the Kakizaki/Matsumae clan (the first three were assuredly of partial Ainu descent). So basically those clans would perhaps be slightly wealthier, but not enough to shift any power balance within Japan or necessarily get them interested in northern expansion.