I am leaving a partial answer here with hope of returning with a more full answer when I am closer to my books.

Allow me to challenge your premise: Alexander the Great is NOT mentioned in the Quran. There are no mentions of his name in any verse at all, nor is he mentioned in the Hadith (the sayings of the prophet). A story that is mentioned in only one place tho, which is highly uncommon occurrence in the Quran, is the story of of Dhul-Qarnain. An ancient conqueror and ruler to whom the defeat and imprisonment of Gog and Magog is attributed in the Quran. Whenever the claim that Alexander the Great is mentioned in the Quran, it is the story of Dhul-Qarnin in question. However. no evidence exists to suggest that Dhul-Qarnin and Alexander the Great are one and the same Person. In fact, many Islamic scholars and historians have spoken in length to refute the matter.

The story of Dhul-Qarning was mentioned in the Quran in one chapter/Surra, Chapter 18 The Cave. In the earliest days of the Islamic preaching in Mecca, Quraish the tribe that controlled Mecca sent two messengers to the Jewish Rabbis in Medina to ask about the validity of Prophet Mohammed's message. Although most were not Jewish, Arabs during that period believed that Rabbis still held true knowledge of the Holy. Given that Paganism was the prominent religion during the time, Quraish's view of knowledge possessed Rabbis was a complicated one. The prominent follower of the prophet Ibn Abbas says that when Quraish asked the Rabbis of Medina of a method to verify whether Mohammed was a true Prophet, the Rabbis answered:

"Ask him about three things which we will tell you to ask, and if he answers them then he is a Prophet who has been sent; if he does not, then he is saying things that are not true, in which case how you will deal with him will be up to you. Ask him about some young men in ancient times, what was their story for theirs is a strange and wondrous tale. Ask him about a man who traveled a great deal and reached the east and the west of the earth. What was his story and ask him about the Ruh (soul or spirit) – what is it? If he tells you about these things, then he is a Prophet, so follow him, but if he does not tell you, then he is a man who is making things up, so deal with him as you see fit."

Chapter 18 of the Quran was the answer to all of these questions, with the story of Dhul-Qarnin being that of the man "who traveled a great deal". Note that neither the Rabbis, Ibn Abbas, nor the verses of the chapter mentioned the name of Alexander the Great. More importantly, Dhul-Qarnain is explicitly listed in The Cave as a theist and a follower of the Abrahamic religion of his era. This last point alone is the single most vocal evidence Islamic scholars use against your premise, given that Alexander the Great was known among Arab scholars as a pagan.

So, where does the misconception come from? More likely than not, because Alexander the Great was also nicknamed Dhul-Qarnin. Dhul-Qarnin in Arabic literally means "the two horned one", which is either understood literally or as possessing two strong fronts. Islamic scholar Ibn Hajr was quoted saying:

"The Greek Alexander [the Great] was closer to the birth of Jesus Christ, which was more than two thousand years after Abraham's. Clearly, Alexander also held the nickname Dhul-Qarnin as a reference to his processor as they were both wildly successful conquerors; that or for his victory against the great Persian and Roman empires. The truth is, the one [Dhul-Qarning] who Allah told the story of in Quran came long before [Alexander].

The differences include: the aforementioned [time difference]; second that Alexander was a Pagan, a student of Aristotle, whom opinion he follows, and was definitely a Kafir; and third that Dhul-Qarnin was of Arab [Semitic] origin, while Alexander was a Greek."

Islamic historian Ibn Kathir also said:

"Ibn Zuraiq, and other sources, mentioned that Dhul-Qarnin met Abraham and followed his religion, then visited the Ka'ba [in Mecca] with him and Ismail.

As for the Macedonian, Egyptian, builder of Alexandria [Dhul-Qarnin], who the Romans name the days after, he was born a great deal of time after the former. [Alexander the Great] came merely three hundred [and a few] years before Jesus Christ, had Aristotle as his teacher and minister, and defeated both Darius and kings of Persia quite the painful and humiliating defeat.

Here, I list them both, for they are often mistakenly thought to be one by commoners [...]"

In conclusion, both Alexander the Great and Aristotle were pretty well known to Islamic scholars and the public at the time, enough for a misconception among commoners to occur. But virtually no worthy source supports the claim that either were mentioned in the Quran. I'll try to get back to the second part of your question when I have the time but for now I can answer any related questions.