Yes, but I asked specifically about their trade networks.
Okay, then. I'll see what I can find.
The Varyags got across the rapids of Volkhov, the long water divide between Lovat and Dnepr, and the rapids of Drepr. All the while confronted by locals who could use all the same cultivated plants, domestic animals and metals.
But that was Slavic territory already familiar to the Norsemen. That area (from Rusь northwards) had long been a part of the history of that area, and hence why they went through that area with ease. Umbral is right on this one - the North Atlantic is on the other end of a supply chain into an area unfamiliar to them, hence fewer settlers (and why I keep insisting on the population factor as being key to Vinland). This is even more so since I don't think Mississippian culture trade networks extended to the area of modern-day Atlantic Canada.
Yes, probably.
For a surplus inhabitant of Iceland or Greenland, Newfoundland would be the closest and most practical place to go and farm. The island is slightly bigger than Iceland, but with better climate - just slightly warmer summer, flatter and lower landscape, tall-growing forests...
Few Norse would go past Newfoundland compared to those who settle down there.
There you go.
Iceland, with 20 000...30 000 souls from 11th century on, sent out 1000 settlers to Greenland in 986, and more in later years. It would be easy for Iceland to send 100 emigrants each year to Newfoundland through 11th century, so 10 000 souls in total, plus their natural increase - by 1100, there would be more Norse in Newfoundland than in Iceland.
OK, that's one bit.
Iceland got a bishop in 1056. In 1106, northern Iceland got a separate Bishop of Holar. And in 1126, Greenland got a separate bishop.
In late 11th century, founding a bishopric in Newfoundland would be likely, for a Christian Vinland. And the size and population would quickly warrant extra bishops - plus bishops in the far away Norse trading settlements in Cape Breton, Montreal, Massachusetts...
That could work.
It is not so important whether the men are "immigrants". What is more important is what they do once they have arrived.
Actually, I would argue the opposite - it is a pattern that is consistent with a particular style of language development. Whether the men are "immigrants" or not is actually pretty important, particularly when dealing with pidgins, creoles, and the like. If we accept Celtic influence on Icelandic (a notion that is controversial unto itself), for example, then it could be argued that Icelandic itself is a Norse-Celtic hybrid language with heavy Norse influence on phonology and grammar. In the case of Michif, an unusual mixed language which became more complex instead of simplifying due to the interaction of French and Cree elements, "bound" elements (i.e. verbal morphology) is of Cree origin and is thus polysynthetic in nature, whilst "free" elements (i.e. nominal morphology) are divided between words of Cree origin and words of French origin (i.e. lom "man" < French l'homme "the man"). A similar development in Michif could also occur hear, though possibly with a few differences.
If the Norse in Vinland become full-time traders, wandering around rivers and forests then, yes, they have little opportunity to teach their children.
If, however, they stake out small and demarcated plots of land (like isles of Boularderie, Orleans, Montreal, Wolfe, Aquidneck...), and engage in intensive agriculture there (fields and haymaking) while the more extensive roaming occupations like providing fish and game meat are left to their Skraeling trade partners and in-laws, they stay around home somewhat longer at agricultural work.
True - and sociological context is almost always taken account into describing the development of a language, especially in historical linguistics.
Did the people of Normandy end up speaking standard French like the French of Picardy and Ile de France never conquered by Norse, or a Norse-French creole language?
Both: their main language - and its offshoots Jèrriais, Dgèrnésais , et autres langues - is essentially a Norse-Old French creole language (one which has left a mark in several European languages, including non-Indo-European ones like Maltese), whilst nowadays most Normans are also fluent in le français standard.
What about Orkneys and Shetlands, which must have had Celtic settlers since Neolithic?
Scots-speaking, though with a noticable Norse influence.
I'm surprised you didn't mention some Scottish Gaelic-speaking island which had the only variety of Scottish Gaelic with tones, not to mention that Scottish Gaelic in general has an aspiration contrast instead of Irish's voicing contrast (i.e. /ph/-/p/ in Scottish Gaelic vs. /p/-/b/ in Irish for the labial stops <p> and <b>).