These questions are sort of like asking which government - India or Pakistan - is correct in claiming the Kashmir region. In other words, the issues seem to be a matter of opinion depending on which country the answerer comes from. Most North Americans are taught that there are 7 continents: Asia, Africa, North America, South America, Antarctica, Europe and Australia/Oceania. In some textbooks, North and South America are combined into "America" and/or Europe and Asia are combined into "Eurasia", for a grant total of 6 or even 5. (I was taught there are 6 continents, with Europe and Asia combined.) What it all comes down to is how the text book author defines "continent" .

Is it one continuous land mass, or merely a "principal" or "major" land mass? If you go with the first definition, a continuous mass of land, then North and South America would have to be combined, as would Asia and Europe, generating only 5 continents. If you go with the second, more vague definition, a large land mass, then what constitutes a continent is open to interpretation. The Latin root of continent suggests "continuous", but many dictionaries use the second, more vague definition. The Oxford English Dictionary, the mother of all dictionaries, defines continent as "a connected or continuous tract of land".

According to the OED, the first time the word continent was used in print, in 1559, it was thus: "Continent..is a portion of th' Earth, which is not parted by the Seas asounder". It seems your class should take a vote! The middle east is part of the continent of Asia or Eurasia, depending on how you were taught. Egypt is considered part of Africa. Like "orient", the terms "near east", "middle east" and "far east" are descriptive terms, and official definitions probably don't exist. According to the Oxford English Dictionary: Near East: "A region comprising the countries of the eastern Mediterranean, sometimes also including those of the Balkan peninsula, south-west Asia, or north Africa." Middle East: "States lying between the Near and Far East, esp. Egypt and Iran and the countries between them."
Far East: "The extreme eastern regions of the Old World, esp. China and Japan."

Most people tend to agree that North America collectively refers to Greenland, Canada, the US, Mexico and Central America. The line stops at Colombia. Hawaii is considered part of Oceania, a group of islands in the South Pacific which are sometimes lumped with Australia and sometimes ignored.

Here is the answer from an "international": It does not really matter: If you include Antarctica, there are 7 -- Asia, North America, South America, Africa, Europe and Australia and Antarctica. If you don't include Antarctica (because no one lives there) there are 6. Egypt is in Africa (the north-eastern tip). Geographically, it cannot be called middle-eastern. Culturally and politically, it is more middle-eastern than African. The Middle-East is also called West-Asia, because it is in Asia, and in the west. Central America is usually considered South America. The North is USA, Canada and Mexico.