The student made some pretty serious factual errors in that speech, I'm afraid.
"To illustrate, the hwaet of Old English lost the initial H sound to become the what of today."
The what of today DOES have the initial H sound. Say it, you'll hear it. We write it with the letters reversed from the way we say it: it's pronounced HWAT.
"Notice that he was called William, rather than the French equivalent, Guillame."
No, he wasn't. He was called "Guillaume le batard" or "Guillaume le duc" or "Guillaume de Normandie," in French. The Normans, although of Viking ancestry, by 1066 spoke French, not a Scandinavian tongue. Guillaume has been Anglicized to William for English students of history, because he became King of England, but in his time he was always called Guillaume.
"Overall, English became a trilingual country where English, French, and Latin were all spoken. However, after the Black Death the surviving common people became more valuable due to the scarcity of labor. As a result, the laborers native tongue of English assumed even a greater proportion among the three languages."
Not quite. England was never really a "trilingual" country. Latin was the language of the Church service and of serious scholarship (that was true throughout western Europe, not just in England). But it was not a language commonly spoken, even among scholars. French was the language of the court and the nobility, English the language of the common people. The overwhelming majority of the people spoke English, not French or Latin, but if you wanted to get anywhere with the ruling class, you needed to speak French as well, and if you wanted a career in scholarship or the Church (not just in England but throughout western Europe) you needed to read and write Latin. The typical Norman noble, though, was not literate in Latin (or in French or English, commonly), nor was the typical peasant or townsman.
Over time, the Norman aristocracy ceased thinking of itself as Norman or French and started thinking of itself as English. It's conceivable the Black Death contributed to this, but it certainly wasn't the sole cause. Anglo-Norman (the Old French dialect of the conquerors) remained the language of the English court until the 15th century, although literature resurfaced in Middle English in the 14th (e.g. Chaucer). By the time of the Tudors, the transformed English language had replaced Norman French as the court tongue.
The Great Vowel shift is indeed the main difference between Middle and Modern English, a difference in pronunciation rather than in writing. But the sample presented at the beginning of the OP is in Old English, not Middle English. To see a good sample of written Middle English, go here:
http://www.fordham.edu/halsall/sourc...olog-para.html As you can see, although it's quite archaic, the written version of Middle English is recognizable as English and is not so radically different as to be considered a foreign language, while Old English is completely indecipherable to modern English speakers.