Die kalte Luft macht meine Wange rot.

Because German usually uses an article with a singular noun when talking about a specific thing or a general concrete thing in a full sentence.

• die Luft = the air
• kalte Luft = cold air (more like a noun phrase without the article)
• die kalte Luft = the cold air

Here, die is also helpful because it shows that Luft is feminine.

Because adjectives in German change their endings depending on:

• the article before them
• the gender of the noun
• the case of the noun
• whether the noun is singular or plural

In die kalte Luft:

• Luft is feminine
• it is singular
• it is in the nominative case
• it has the definite article die

After die in this situation, the adjective takes -e:

• die kalte Luft
• die rote Wange
• die frische Luft

This is a normal example of weak adjective endings.

Because Luft is the thing doing the action in the sentence.

The verb is macht from machen, and the structure is:

Something makes something else adjective

So in:

Die kalte Luft macht meine Wange rot.

• Die kalte Luft = subject
• macht = verb
• meine Wange = object
• rot = result adjective

A useful way to test the subject in German is to ask Who or what does the action?

• What makes the cheek red?
  Die kalte Luft.

Because meine Wange is the direct object here, so it is in the accusative case.

The noun Wange is feminine, and the possessive determiner mein- changes depending on case.

For feminine nouns:

• nominative: meine Wange
• accusative: meine Wange
• dative: meiner Wange
• genitive: meiner Wange

So meiner Wange would be dative or genitive, not accusative.

Since machen here takes a direct object, German uses the accusative:

• Die kalte Luft macht meine Wange rot.

Not necessarily. German often uses the singular if only one cheek is meant, or if the sentence is just describing the effect in a simple way.

• meine Wange = my cheek
• meine Wangen = my cheeks

If both cheeks are meant, you could say:

• Die kalte Luft macht meine Wangen rot.

The singular version is still perfectly natural if the speaker is talking about one cheek.

Because rot is not being used directly before a noun here. It is acting as a predicate adjective, describing the result of the action.

Compare:

• die rote Wange = the red cheek
  Here rote comes before the noun, so it needs an adjective ending.

• Die Wange ist rot. = The cheek is red.
  Here rot comes after the verb, so it does not take an ending.

• Die kalte Luft macht meine Wange rot.
  Same idea: rot is a predicate adjective showing the result.

So macht ... rot means makes ... red.

Yes. Very common.

German often uses machen + object + adjective to mean make something become ...

Examples:

• Das macht mich müde. = That makes me tired.
• Die Sonne macht das Zimmer warm. = The sun makes the room warm.
• Der Witz macht ihn glücklich. = The joke makes him happy.
• Die kalte Luft macht meine Wange rot.

So this sentence follows a very useful pattern.

No, that would sound wrong here.

The normal adjective is rot. German uses the basic color adjective after machen:

• macht meine Wange rot

There is a word rötlich, but it means more like reddish, not simply red, and it would not be the normal choice in this sentence.

So stick with:

• rot = red
• macht ... rot = makes ... red

Because in a normal German main clause, the finite verb usually comes in position 2.

Here the sentence starts with the subject:

1. Die kalte Luft
2. macht
3. meine Wange rot

That is standard German word order.

You can move other parts to the front for emphasis, but the verb still stays in second position:

• Meine Wange macht die kalte Luft rot.
  This changes the meaning, so it is wrong for this situation.

• Rot macht die kalte Luft meine Wange.
  Very unnatural.

So the normal and correct order is:

• Die kalte Luft macht meine Wange rot.

No, because Luft is a feminine noun.

Its article is:

• die Luft

So the correct phrase is:

• die kalte Luft

not:

• das kalte Luft
• der kalte Luft

This is something you simply need to memorize with the noun:

• die Luft = feminine
• die Wange = feminine

The dictionary form is machen.

macht is the third person singular present tense form:

• ich mache
• du machst
• er/sie/es macht
• wir machen
• ihr macht
• sie/Sie machen

Since die kalte Luft is singular, the verb must be singular too:

• Die kalte Luft macht ...

Usually yes, but it specifically means the cheek on the face.

So:

• die Wange = cheek

German also has some body-part vocabulary where English and German do not always match perfectly in usage, but in this sentence Wange is the natural word.

If you are learning body parts, it is useful to remember:

• die Wange = cheek
• das Gesicht = face
• die Haut = skin
• die Lippe = lip

Yes, that is also possible in German, and it is actually a very natural body-part pattern.

German often uses:

someone in the dative + body part

So you may hear:

• Die kalte Luft macht mir die Wange rot.

Literally, that is something like:

• The cold air makes me the cheek red

But natural English would still be:

• The cold air makes my cheek red

Both patterns can exist in German:

• macht meine Wange rot
• macht mir die Wange rot

The version with mir die Wange is especially common because German often prefers the dative possessor with body parts.