Learn English – Why don’t adjectives agree with nouns in English

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.

List of adjectival and demonymic forms of place names

The following is a partial list of adjectival forms of place names in English and their demonymic equivalents, which denote the people or the inhabitants of these places.

The list can be found here on Wikipedia

Note: Many of these adjectivals and demonyms are not used in English as frequently as their counterparts in other languages. A common practice is to use a city's name as if it were an adjective, as in "Vienna Philharmonic Orchestra", "Melbourne suburbs", etc.

New York can also be used as an adjective without changing it's form.

A map of adjectival forms of place names

can be found here