Yes, this is basically considered fact. American is old-English. The same with Québécois and French.
By the way, the term "Old English" strictly speaking refers to this: https://en.wikipedia.org/wiki/Old_English. No-one is claiming that Americans speak this language.
IOW, Parisian French also retains some primitive features that have largely disappeared from one Canadian region or another. But we don't talk about those as much. I'm guessing because doing so wouldn't jive well with certain stereotypes about Québec being a backwards hinterland.
This is simply nonsense.
That the current accent is driven by a particular fad aimed at highlighting upper class status doesn't imply that class distinctions are novel, just the particular effort to demarcate them (which wasn't durable, obviously, as RP isn't exclusive to the upper classes.)
No one, AFAICT, did that. The reference to “modern British English” is not, as I read it, a reference to “the current diversity of British accents”, but rather “the current dominant British accent”.
Fair point - I would also agree that the idea of a "dominant" British accent seems a bit odd - certainly not in terms of what people actually sound like (rather than the broadcast media).
In a highly class-conscious society where the vast majority of people spoke English as their first language, it seems fairly unlikely that accent would have had no connotation of social status.
It thus seems hard to believe that the development of the modern diversity of English dialects would have been spurred by some sudden need to mark class distinctions.
Believe it or not, there is an entire field called linguistics that studies human language and how it evolves.
In terms of lexicon, much of the archaic flavour is actually the result of 19th-century language reformers trying to restore old words. In the meantime, Icelandic had borrowed heavily from Danish.
Indeed, there is the field of linguistics, and scholarly treatments of Icelandic (as opposed to pop-sci presentations of the language as a time capsule like yours) point out that Icelandic has undergone a great deal of innovation like any other North Germanic language.