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.
I think it simply follows from the natural stress patterns of the English language. See here. Two syllable nouns generally have the stress on the first syllable. Many 3 syllable nouns also do. Words that depart from the natural stress patterns tend to be words borrowed from other languages, and there is a tendency for them to eventually get coerced into the native pattern if they are in the language long enough.
There might be something of interest to explore if female names are more likely to depart from that pattern--there may be a greater tendency to want to use foreign names or foreign pronunciations with female names, having to do with cultural notions of masculinity and feminimity (e.g. good Saxon words considered to sound manly, vs fancy French words).
Best Answer
The word for the colour yellow comes from a germanic root as well.
Palatalization is a sound change that took place from Old English to Modern English. Here's a short list of words where this shift took place: day (German Tag), yarn (German Garn), way (German Weg), year (Old English gear), nail (German Nagel), yield (Old English geldan, Old High German geltan) and thirsty (German durstig). It also happened with another colour word: gray (Old English græg.)
It should be noted that in Modern German, the terminal g has become devoiced and Tag sounds more like tuck in English.
The word is similar in Latin languages because they all share the same Proto-Indo-European root, *ghel-. It's interesting that this same root which had the meaning "to shine" gave us not only the colour yellow, but also gold, gild, gall (i.e. yellow-coloured bile), and a range of sparkly gl- words: glitter, gleam, glow, etc.