Learn English – What happened around 1700 that transformed / changed the English language

Yes, grammar rules have changed considerably over the years. Original Chaucer is barely comprehensible to those used to just modern English; patches of Shakespeare and his contemporaries are a little stilted to modern eyes; even authors as recent as, say, Dickens or Austen write in a style that is somewhat different from the modern style. However, the more recent authors are much more readily comprehended than the more ancient authors.

However, there is also perhaps more continuity in the grammar rules than in spelling. That is, many key aspects of English grammar were also present in the Medieval period; a lot of the time, it was just the spellings and inflections on words that was different. There's some gross over-simplification in there.

I'm not sure that 'caste' is the correct term to use; 'class' certainly would be more normal. The main difference between the speech of 'peasants' versus 'clergy' or 'noble' would be in degree of literacy. Depending on the exact era, one factor might be that the 'noble' would speak French first, maybe Latin second, and English possibly a poor third - in the (first half of the) 12th Century, say. The clergy would probably speak all three contemporaneously, but would certainly know Latin since the liturgy was all Latin at the time. The 'peasants' might very well not really understand Latin properly, though they might well recognize passages from church; they'd speak English, but probably not French.

A couple of books I have that are fairly accessible (not too hard to read) and may be of interest:

• "Our Language", Simeon Potter, published by Pelican. I have what appears to be a 1950 1st Edition (cost one shilling and sixpence; it looks like I got it secondhand for 30 pence), but it is still available on Amazon in more recent (1976) editions.
• "The English Language", Robert Burchfield, published by Oxford. Also available via Amazon, but apparently out of print.

The source you cite seems to confuse two different sources of Danish influence in the English Language: the Jutes and the Danes.

• The Jutes are one of the peoples who invaded Britain from 449 onwards, along with the Angles, the Saxons and the Frisians.
• The Danes came as a second wave 4 centuries later (roughly from 850 to 878) and, as shown in @Robusto's answer, carved themselves the kingdom named the Danelaw.

The confusion comes from the fact that modern Denmark and Jutland are today the same place. However it is not certain that the Jutes came from modern Jutland. Let me quote an excerpt of the book "Origin of the English Language - A social and Linguistic History" [p. 53]:

"So it was first thought that the Jutes came from what we now call Jutland; the Angles from the western side of the Jutish peninsula and the east bank of the Elbe; the Saxons from the Elbe to perhaps the mouth of the Rhine. More recent Archaeological evidence locates the Angles farther south-east and the Jutes on the coast, near the Frisian islands off the coast of Germany and the Netherlands"

As a matter of fact, the real identity of the Jutes and their place of origin cannot be reliably established just from ancient texts because they contradict each other. Venerable Bede for instance, often cited as a source lived more than 250 years after the Anglo-Saxon migrations. If you hypothesise that the Jutes migrated to Jutland after the 5th century then the Wikipedia article stating that "many Danish speakers are able to understand some spoken Frisian" makes perfect sense. After all, people migration and splitting was quite common in these times. Consider for instance the migration of Goths, splitting and then travelling to Spain, Italy and Russia or that of the Vandals: to Sicily through Spain, Morocco and Tunisia.

Furthermore, as you have rightly pointed out, the distance between the Frisian islands and England is much shorter than the distance between modern Jutland and England. The most convincing observation is that the Jutes are said to have landed in Kent... That is quite possible if they came from Friesland but less likely if they came from Jutland. The Danelaw does lie "in front" of Denmark but Kent surely doesn't.

I do not mean to underestimate the contribution of Old Norse to English; it is instead, well established. One often cites for instance many words in "sk": (sky, score, skirt, skill, scab, scale, scrap), or such important words as get, die, call, egg, raise, take. Nevertheless one has to be careful when ascribing the etymology of an English word to Danes. It could be from Danish influence or it could be of more ancient Anglo-Saxon origin.

As for ta and thank, the origin of thank is believed to be Proto Germanic (thankojan) and was already present in Anglo Saxon English before the Danish invasions. However, the Old English (þancian) and Old Norse (þakka) versions followed parallel evolution paths and met again when Danes landed in Britain. So yes "ta" looks like Old Norse indeed but it caught up because it met an already well established cognate.