I have some questions for you, and since you are a scholar,
I hope you can please answer them for me.
1 - What is the real reason the majority of scholars say that a Muslim woman can't marry a non-Muslim?

This is because they follow the old tradition. This tradition was written in the middle ages reflecting the fanatic holy war between Muslims and the Christians in that time. They used to twist the meanings of the holy Quran and fabricate sayings and attribute them to the Prophet Mohammed, two centuries and more after his death. The Wahabism has restored this Middle-aged culture and spread it as the real Islam. By the Saudi influence, the Quranists are persecuted because they are calling to understand the Holy Quran according to its terminology and terms. The Quranic movement is suffering now arrest and persecution in Egypt because it works for reform Muslims from within Islam.

2 -What is the meaning of "mushrikat" as used in 2:221?
According to the Quranic terminology it means the terrorist one , and /or the one who support terrorism. Terrorisim ( or killing the innocent people ) in Islam means ( Shirk and Kofr ) or infidelity.

3- Does the Quran really forbid a Muslim woman from marrying People of the Book?
Any peaceful human is Muslim regardless of his faith or belief.
If the Christian (or the Sunni Muslim) is terrorist he becomes infidel according to his behavior. So, it is prohibited to marry him or her.

4- If I marry someone who is non-Muslim, am I no longer considered to be a Muslim?
You are Muslim as long you are peaceful in your behavior, and you are Muslim in your heart as long you believe in God alone, without any idol with Him.
Being Muslim in behavior and /or in heart has nothing to do with your marriage. Every human is responsible for his own deeds and belief. As a woman, you are independent human with and without husband.

5- Is it true that Aiysha was engaged to be married to a Christian man before marrying Muhammed (PBUH)?
It is a fabrication.

6 -How did the Prophet (PBUH) treat women who were married to non-Muslims?
The Prophet Mohammed has nothing to do with them. Some of his ardent enemies (The Hypocrites) lived in Al Madina under his authority as the leader of the State in that time. According to the unlimited freedom of speech and belief in Islam , every one is free to say and in believe as he chooses as long he does not compel other in religion , and /or persecute them and /or kill them unjustly.

7- Did he ever make anyone, man or woman, end their marriage because they weren't married to Muslims?
Absolutely not.