Har hun nogensinde været her?

Because this is a yes/no question in Danish. In main-clause yes/no questions, the finite verb normally comes first, followed by the subject.

So:

• Statement: Hun har været her.
• Question: Har hun været her?

This is similar to English Has she been here?

It is the present perfect.

It is formed with:

• har = present tense of have
• været = past participle of være

So the pattern is:

• har + past participle

Examples:

• Hun har spist. = She has eaten.
• Hun har været her. = She has been here.

Because Danish is expressing the idea of has been, not is or was.

• er = is
• var = was
• har været = has been

So:

• Er hun her? = Is she here?
• Var hun her? = Was she here?
• Har hun været her? = Has she been here?

The last one asks about her presence at some time before now.

Nogensinde means ever.

It is used when asking whether something has happened at any time up to now.

So in this sentence, it strengthens the idea:

• Har hun været her? = Has she been here?
• Har hun nogensinde været her? = Has she ever been here?

It is very common in questions with the present perfect.

It usually comes after the subject and before the past participle or other main verb material.

So this is natural:

• Har hun nogensinde været her?

A useful pattern is:

• Har + subject + nogensinde + past participle + ... ?

Examples:

• Har du nogensinde set det?
• Har I nogensinde prøvet det?

Other word orders may sometimes occur for emphasis, but the version in your sentence is the normal one to learn first.

Været is the past participle of være, which means to be.

Forms of være include:

• infinitive: være
• present: er
• past: var
• past participle: været

So:

• hun er her = she is here
• hun var her = she was here
• hun har været her = she has been here

Yes. Danish her means here.

This is a common point of confusion for English speakers because English her usually refers to a woman, but in Danish her is a place word.

Compare:

• Danish her = here
• Danish hende = her (object form)
• Danish hendes = her / hers

So in this sentence, her is about location, not a female person.

Hun means she.

It is the subject pronoun, so it is used because she is the person doing the action of having been somewhere.

A quick comparison:

• hun = she
• hende = her

Examples:

• Hun er her. = She is here.
• Jeg så hende. = I saw her.

In your sentence, hun is the subject, so hun is the correct form.

Yes.

• Har hun været her? = Has she been here?
• Har hun nogensinde været her? = Has she ever been here?

Without nogensinde, the question is more neutral. With nogensinde, it specifically asks about any time at all.

A short answer would often begin with ja or nej:

• Ja, det har hun. = Yes, she has.
• Nej, det har hun ikke. = No, she hasn’t.

A fuller answer could be:

• Ja, hun har været her før.
• Nej, hun har aldrig været her.

Notice that Danish often uses det in short answers like Ja, det har hun.

These two words can be tricky for learners.

A rough guide:

• nogensinde sounds approximately like NO-gen-sin-de
• været is roughly VAIR-eth or VEH-reth, depending on accent and speaking style

A few pronunciation notes:

• æ is a vowel English does not have exactly
• r in Danish is often softer than in English
• final syllables may sound weaker than you expect

Also, her is not pronounced like English her. Its vowel is different in Danish.

It is similar in meaning, but the grammar is a little different.

English:

• Has she ever been here?

Danish:

• Har hun nogensinde været her?

Both languages put the auxiliary verb first in a yes/no question:

• Has / Har

But Danish learners should pay attention to where words like nogensinde go. Danish word order is often stricter than English learners expect.

Yes. That means Has she been here before?

It is close in meaning, but not exactly the same as nogensinde.

• nogensinde = ever, at any time at all
• før = before

So:

• Har hun nogensinde været her? asks whether it has happened at all
• Har hun været her før? asks whether she has been here previously

In many real situations, both are possible, but nogensinde sounds a bit broader or more emphatic.