Jeg børster mit hår hver morgen.

Because hår is a neuter noun in Danish: et hår.

With singular possessives, Danish changes the form depending on the noun’s gender:

• min for common-gender nouns
• mit for neuter nouns
• mine for plural nouns

So:

• min bog = my book
• mit hår = my hair
• mine sko = my shoes

Børster is the present tense of at børste = to brush.

A very common Danish pattern is:

• infinitive: børste
• present tense: børster

So Jeg børster means I brush or, depending on context, I am brushing.

In this sentence, because of hver morgen, it clearly describes a habit: something you do regularly.

Danish usually does not separate simple present and present progressive the way English does.

So Jeg børster mit hår can mean:

• I brush my hair
• I am brushing my hair

The context tells you which meaning is intended.

Here, hver morgen makes it a routine, so the natural English meaning is I brush my hair every morning.

Because mit already acts as the determiner.

In Danish, you normally do not combine a possessive with a separate article or definite ending. So you say:

• mit hår = my hair

not:

• det mit hår
• mit håret

This is similar to English: you say my hair, not the my hair.

Because hver means every/each, and after hver Danish uses the noun in the singular indefinite form.

So:

• hver morgen = every morning
• hver dag = every day
• hver uge = every week

You do not use the definite form after hver, so hver morgenen is incorrect.

Because sit/sin/sine is only used with a third-person subject.

Use:

• min/mit/mine with jeg
• din/dit/dine with du
• sin/sit/sine with han/hun/den/det/de when it refers back to that subject

So:

• Jeg børster mit hår. = I brush my hair.
• Hun børster sit hår. = She brushes her own hair.

A native English speaker often wants to use sit for any reflexive idea, but in Danish it is restricted to the third person.

Here it functions like a collective/mass noun, meaning hair in general.

Danish can use hår this way even though et hår can also mean a hair.

So:

• et hår = one hair
• mit hår = my hair, as a whole

This is similar to English, where hair can also be mass noun: My hair is wet.

Yes. A very natural alternative is:

Hver morgen børster jeg mit hår.

This shows an important Danish word-order rule: the finite verb usually stays in second position in main clauses.

So when hver morgen comes first, børster must come before jeg:

• Jeg børster mit hår hver morgen.
• Hver morgen børster jeg mit hår.

Both are correct.

Yes, that can also sound natural.

When it is obvious whose body part you mean, Danish often allows the definite form instead of a possessive:

• Jeg børster mit hår hver morgen.
• Jeg børster håret hver morgen.

The version with mit hår is more explicit about ownership.
The version with håret can sound a bit more neutral or idiomatic in context.

Both are understandable and correct.

At børste most directly means to brush.

If you want to be more specific about using a comb, Danish may use other verbs such as at rede or sometimes at kamme, depending on context.

So in this sentence, the most direct idea is brushing your hair, not necessarily combing it with a comb.