It depends on what you mean by "capitalized".
If you are referring to the use of majuscule or upper-case letters, YES. The "Middle East" as a region is a proper noun and should always be capitalized.
If you are referring to the injection of money or capital into a region, it depends. There are a number of areas of the Middle East, especially in the Persian Gulf Region, where the export of petroleum has provided the funds to capitalize other areas of the economy and countries like the United Arab Emirates and Kuwait have invested those petroleum funds in other areas of the economy. While they do not need capitalization, their nascent diversification could benefit from it. There are a number of countries like Syria, Iraq, Yemen, and Libya which are in the middle of civil war (as of April 2016) and have no economy to capitalize. Finally, there are a number of countries like Israel, Turkey, Jordan, and Tunisia which have functioning economies and no endemic source of investment. These countries are worth injecting capital into in order to both promote technological and industrial development and to promote stability in the region.
It should be capitalized when using it to refer to the place the Middle East.
No, "secondary students" should not be capitalized in the middle of a sentence unless it is a proper noun or at the beginning of a sentence.
No, "polar" should not be capitalized when used in the middle of a sentence. It should only be capitalized if it is the first word of a sentence or part of a proper noun.
Yes, "Middle Ages" should be capitalized when referring to that specific historical period, as it is a proper noun.
The capital letter is used when referring to a territory situated in this direction, such as the Far East
Yes; it is written as Middle East when you use it.
It should be capitalized when using it to refer to the place the Middle East.
No it shouldn't be capitalized.
Yes, "Middle Ages" should be capitalized when referring to that specific historical period, as it is a proper noun.
No, "secondary students" should not be capitalized in the middle of a sentence unless it is a proper noun or at the beginning of a sentence.
No, "polar" should not be capitalized when used in the middle of a sentence. It should only be capitalized if it is the first word of a sentence or part of a proper noun.
It should be capitalized when it forms part of a country name.
The capital letter is used when referring to a territory situated in this direction, such as the Far East
Yes, it should be capitalized.
No - it is just good evening.
No, the word "winter" should not be capitalized in the middle of a sentence unless it is at the beginning of a sentence or part of a proper noun.
No, "methadone" should not be capitalized unless it is at the beginning of a sentence or part of a proper noun (such as a specific brand name).