"After the time of the Norman conquest, Old English developed into Middle English, borrowing heavily from the Norman-French"
Which only applied to higher castes and the nobilty through claims of the throne by france. The whole Robin Hood myth is build upon those claims and the anglo-saxon population acted against it.
Later some, a very small amount, influenced the english language as of today because of this short regency. For example "pig". "Swine", the alternative comes from a former "Schwein" (german).
The grammar, the structure of the language is not latin. The language derived from a very early german. If you read "Beowulf" or even "Lord of the Rings" (Tolkien was a Germanist) you find espacially the same names and word stems than in middle high german.
Ask every linguist in the world.
"These differences, though minor, preclude mutual intelligibility, yet English is still much closer to other Germanic languages than to languages of any other family."
breakfast = Fastenbruch
morning = Morgen
wolf = Wolf
bear = Bär
way = Weg
stone = Stein
street = Straße
world = Welt
star = Stern
The list goes on for a great number of words. Especially very old words (words that have been used for thousands of years and independent of which time by humans) are easily comparable.
Some words like "Fastenbruch" are rarely used even in modern german because there are many developments in a language. The differences between the east german "Sächsisch" (a dialect) and todays english is just 1500 years of nearly independent development. There are scandinavian occupations (which is also germanic languages but this time not western but north germanic), so not far away, but also a short period of french leadership which influenced the language in the middle ages.
Both examples did not influenced the original language which had other influences. So all the difference is time. I really know what I am talking about. ;)
"The Anglo-Saxons were in no way like today's Germans. Nor were they very similar to Old Germans. They were cousins, though. "
Absolutely wrong!
The saxons are one of the greater tribes that effectively and directly became the german people. The whole history untill the late 1800s are dominated of small german states that directly go back to those tribes. Franks, Saxons, Allamanics, Bajuwarians are just the more important tribes. To declare the Saxons as "cousins" is just plain wrong.
Other popular german tribes like the Vandals, the Goths formed kingdoms in Spain, even Africa.
The Franks (Frankfurt/Frankenfurt means a fordable spot in the course of a river and is named after them, also "Frankreich"/"Frankenreich" or "france") was founded by Charles the Great. "Karl der Große" is a frank and first king of the later "Roman Empire of the German Nation".
It collapsed in three parts (three sons) and the western one became france. The other two became Germany.
This all just is supposed to show that those tribes were not just a few people that lived on the spot where Germany is today. Germans are the direct (!) descendents of those. The Anglo-Saxons, Englanders, that live in England, not Great Britain, if you want to draw that line, are the cousins. The ancestors of them were the same people like the ancestors of today's Germans. But this is very simplified to clarify. There are a lot of celtic influences through the original population of Ireland, Scotland, Wales and France after the occupations and building of Great Britain which involves these tribes of Celts.
There were three great cultures in Central Europe. Today it is difficult to draw a line especially in Britain.
1. Celts, Western Europe (originally North England, parts of Ireland and the Normandy in France)
2. Germanic Peoples, the English language is a little confusing here, in most germanic languages they are refered to as "Germans" but that describes today's germans in English. The germans call themself "Deutsche", not "Germanen". (originally Denmark, North and East Germany, Scandinavia)
3. Slavs (From Poland to the east to Russia)
There are other minor groups, one big one to the south (Romans) that I skipped.
Those three groups among many others in the world are groups which shared language, culture, religious and other components.
In terms of language you can trace back the following languages to those and in most cases the respective Peoples derive from those three groups.
1. Celts, that means celtic language: (Old) Irish (not dialect in modern English!), (Old) Scottish Gaelic (Same here, nothing to do with English), Gaulish (France).
2. Germanic Peoples, that means germanic language:
North germanic: Norwegian, Swedish, Danish, Icelandic
West germanic: German, Dutch (which derived from german - frisian dialect), English (the whole point, derived from german due to angles, saxons and jutes)
3. Slavs, slavic languages:
Three groups, not this discussion tangenting, the most popular are Russian, Polish, etc.
I hope I could carify what I am talking about.
And to close this all: I recommend to go further in this all by visting some of these links:
http://en.wikipedia.org/wiki/Celtic_languages
http://en.wikipedia.org/wiki/North_Germanic_languages
http://en.wikipedia.org/wiki/West_Germanic_languages
http://en.wikipedia.org/wiki/Slavic_languages