Learn English – How did 7 come to be an abbreviation for ‘and’ in Old English

I just spent some quality time perusing the Insular and Anglo-Saxon chapters of Michelle P. Brown's A Guide to Western Historical Scripts from Antiquity to 1600 (pp. 48-49 and 58-59), as well as pp. 34-42 of Marc Drogin's Medieval Calligraphy: Its History and Technique. The names they use for the scripts are varied and often conflicting, but they seem to agree on something like the following:

Saints Patrick and Augustine imported versions of Uncial and Roman Half-Uncial scripts into Ireland and Britain, respectively, in the early 5th and late 6th/early 7th centuries, again respectively. Those scripts evolved, cross-fertilized, and developed along the usual pattern of utility → formalization → decoration → exaggeration → need for a new utility script. The result was something probably best termed Insular Majuscule; think the Book of Kells or the Lindisfarne Gospels. This continued in use on both islands until the 9th century. Shortly after it appears, the utility version, Insular Minuscule also appears, and by the mid to late 9th century, entirely replaces the majuscule (uppercase) version. At that point, influences from the continent (read: Carolingian minuscule) would lead to a shift in writing styles for Latin documents, but Anglo-Saxon (aka Old English) continued to be written in Insular Minuscule until as late as the 12th century. Of course, Carolingian minuscule itself was developed at the court of Charlemagne under a certain abbot named Alcuin, born in — you guessed it — England.

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.