Hun mister ikke viljen.

Because in a normal Danish main clause, the finite verb usually comes in second position.

So the structure is:

• Hun = subject
• mister = finite verb
• ikke = negation
• viljen = object

This gives:

• Hun mister ikke viljen.

A useful rule is:

• subject + finite verb + ikke + ...

So Hun ikke mister viljen is not correct as a normal main clause.

Mister is the present tense of the verb at miste, which means to lose.

Examples:

• jeg mister = I lose / I am losing
• hun mister = she loses / she is losing
• de mister = they lose / they are losing

Danish does not change the verb for different persons the way English does. So the same present-tense form is used with all subjects:

• jeg mister
• du mister
• han/hun mister
• vi mister
• I mister
• de mister

Viljen is the definite form of vilje.

• vilje = will
• viljen = the will

In Danish, the definite article is often added as an ending:

• en bog = a book
• bogen = the book

Likewise:

• en vilje = a will
• viljen = the will

In this sentence, Danish uses the definite form because it refers to her will / the will in a general but specific sense. With abstract nouns like this, Danish often uses the definite form where English may simply say will.

Because viljen already works naturally here in Danish.

Danish often uses the definite form of a noun where English would use a possessive idea. So:

• Hun mister ikke viljen
  can naturally mean
• She does not lose her will / She does not lose the will

If you said sin vilje, it could sound more literal or shift the nuance. In many cases, the simple definite noun is the most idiomatic choice with body parts, emotions, or abstract qualities.

Ikke means not.

It negates the verb phrase:

• Hun mister viljen = She loses the will
• Hun mister ikke viljen = She does not lose the will

In Danish main clauses, ikke usually comes after the finite verb:

• Han kommer ikke = He is not coming
• Vi forstår ikke = We do not understand
• Hun mister ikke viljen = She does not lose the will

No. They just happen to look alike in writing.

In this sentence, mister is the verb to lose.

The English title Mister has nothing to do with this Danish verb.

Also, in Danish pronunciation, mister here is pronounced like a normal verb, not like the English title.

Yes, that is a very natural interpretation.

The noun vilje can mean things like:

• will
• determination
• resolve
• strength of will

So depending on context, Hun mister ikke viljen could be understood as:

• She does not lose her will.
• She does not lose her determination.
• She does not give up.

The exact English translation depends on context, even if the core meaning stays the same.

Yes, there often is.

Both can mean to lose, but they are not always interchangeable.

• miste is often used for losing something in a broader or more serious sense:

  • miste håbet = lose hope
  • miste livet = lose one’s life
  • miste viljen = lose the will

• tabe is often used for:

  • losing a game: tabe en kamp
  • dropping or misplacing something in some contexts
  • losing money, weight, time, etc.

So Hun mister ikke viljen sounds natural because viljen is an abstract inner quality. Tabe viljen would sound much less natural.

Because Danish does not use do-support the way English does.

English often needs do/does/did in negatives:

• She does not lose the will.

Danish does not. It simply uses the main verb directly:

• Hun mister ikke viljen.

So the Danish pattern is more like:

• She loses not the will
  although the natural English translation is
• She does not lose the will.

Yes, potentially.

The Danish present tense often covers both:

• a present meaning
• a future meaning, if the context makes that clear

So Hun mister ikke viljen can mean:

• She is not losing heart.
• She does not lose her determination.
• She will not lose her determination.

The exact time reference comes from the context, not from the verb form alone.

Usually yes, in standard usage.

Hun is the Danish subject pronoun meaning she.

Examples:

• Hun kommer = She is coming
• Hun forstår det = She understands it

So in this sentence:

• Hun mister ikke viljen = She does not lose the will / She does not lose heart

The object form would be hende = her, but that is not used here because hun is the subject.