1

No.  Because of pressures elsewhere Rome stopped sending support to the Romans in Britannia.  They continued to govern for quite a while after being cut-off, but eventually mixed with the local inhabitants and became the new British, though as noted by Jahtez, the Saxons and later the Danes came and further transformed the population.

2

What I've always understood is that around the late Medieval period people like Erasmus began paying more attention to the wisdom and insights of the ancients whose artifacts, both physical and intellectual influenced much of their culture.  At about the time of the Enlightenment scholarship regarding ancient Rome became a Hallmark of intelligence and instead of repeating local legends about ancient artifacts an interest in research to find out more about these ancestors began to develop.
Eventually it was realized that the Romans based much of their civilization's exceptionalism on imports from the Greeks.  The 15th through 16th Centuries saw a growth in this Classically based intellectualism and from the 17th through 18th Centuries began the growth of what would evolve into the "modern history as a discipline" of the 19th Century.
Of course, there were "histories" dating back a few thousand years.  But in the past, "history" was, if anything, more subject to hearsay and speculation than it is even today.
In the 18th and 19th Centuries history began to become subject to Academic discipline and the concepts of evidence and "proof" that were evolving (and still are) in the disciplines of science.
Much of this was enabled by other changes in Western Civilization like the movable-type printing press, the development of cotton-rag paper, and the rise of the original Middle-class.  Inheritance of Birth was not as great a determinant of success for that rising class as was the Sagacious and Learned mind, both in business and in Society.  In the 18th Century the ability to cite a great authority was most important.  By the end of the 19th Century this was giving way to the ability to cite good research.
Today we still tend to fall back upon the opinions of those seen as great scholars on this or that subject on the assumption that their scholarship makes them more likely to be right than someone without as much scholarship or with scholarship from a less prestigious school, so we are still very much in the transitioning process from authority-based History to History that arises from scholarly discipline ... but we're getting there and maybe by the end of this century, we will mostly rely on this Historical discipline.
So linguistically?  This view would suggest that a good way to one-up the guy who quoted Pliny or Virgo in ancient Latin was to quote Aristotle or Plato in ancient Greek.and we have about four centuries of elitist competition to introduce Greek terms into our discourse and for that to disseminate through the civilization.

3

The only Normans I can recall seeing on TV were the evil rulers of Nottingham in the "Robin Hood" British TV show. Guy de Gisbourne, the Sheriff of Nottingham, the evil Prince John, etc.
They did bring French-style feudalism to England, which was NOT a good thing for the majority of the population, which is to say the peasant class. Things were much freer in Anglosaxon England, which had had only a very short time to rule a unified England, due to those pesky Danes.
Well I descend from Britons and Danes, so perhaps I am not just being bigoted, since I will defend the Saxons over the Normans, and I seem to be neither of those.
The Normans were generally bad news, it seems to me, with the notable exception of the Kings Roger I and II of the Norman Kingdom of Sicily, who allowed the free intellectualism of Moorish Sicily, which they conquered, to continue, this being credited by some with sparking the Renaissance in Italy. It is true that Roger II especially had an intellectual life at his court which we find admirable in its historical context, though it should be noted that he did not allow much of that free-thinking to percolate down to the populace, whose thinking was still strictly controlled by the Church.

4

So, you're saying that, 'Rome stopped sending support to the Romans in Britannia' isn't the result of 'pressure elsewhere'? Which, if you look closely, is what I said - what's your point?
If you're going to be that pedantic you shouldn't speak of the distinct British tribes of the time as 'local inhabitants'. Bavarians and Friesians in northern Europe wouldn't welcome such labeling as wouldn't, to this day, the Xhosa and Zulus.