Har hun svært ved at se langt?

Because this is a yes/no question in Danish.

In a normal statement, you would usually say:

Hun har svært ved at se langt.
= She has difficulty seeing far.

To turn that into a yes/no question, Danish typically moves the finite verb to the first position:

Har hun svært ved at se langt?
= Does she have difficulty seeing far?

This is similar to English Has she... ? or Does she have... ?

Svært ved at is a very common Danish expression meaning:

• to have difficulty doing something
• to find something hard to do

So:

• have svært ved at forstå = have difficulty understanding
• have svært ved at sove = have trouble sleeping
• have svært ved at se langt = have difficulty seeing far

You can think of have svært ved at + verb as a fixed pattern.

Because at is the infinitive marker in Danish, like to in English.

So:

• se = see
• at se = to see

After the expression svært ved, Danish uses at + infinitive:

• svært ved at læse = difficulty reading / difficulty with reading
• svært ved at høre = difficulty hearing

So ved at se here is just part of the structure have svært ved at + verb.

Because langt is being used adverbially here.

In this sentence, langt means far rather than long. It describes the distance at which she can see.

Compare:

• en lang vej = a long road
  
  • here lang is an adjective describing a noun
• at se langt = to see far
  
  • here langt functions like an adverb

So in this sentence, langt is the correct form.

Not in natural English. Even though lang/langt is related to long, the phrase se langt means see far or see into the distance.

This is a good example of where you should translate by meaning, not word-for-word.

So:

• Kan du se langt? = Can you see far?
• Jeg kan ikke se langt uden briller. = I can’t see far without glasses.

Because hun is the subject form of she.

In this sentence, she is the person doing or experiencing the action, so Danish uses hun:

• hun = she
• hende = her

Compare:

• Hun har svært ved at se langt. = She has difficulty seeing far.
• Jeg kan se hende. = I can see her.

So hun is correct because she is the grammatical subject.

They are close, but not exactly the same.

• Har hun svært ved at se langt? = Does she have difficulty seeing far?
• Kan hun ikke se langt? = Can’t she see far?

The first focuses on difficulty.
The second focuses more directly on ability.

In real conversation, both could be used depending on what you want to emphasize.

Yes, but here it means difficult.

Examples:

• Det er svært. = It is difficult.
• Hun har det svært. = She is having a hard time.
• en svær sygdom = a serious/severe illness

In have svært ved at, the meaning is clearly about difficulty, not severity.

It is perfectly natural and neutral Danish. You could use it in everyday speech, writing, or conversation with a doctor or optician.

It does not sound overly formal.

A native speaker might also say similar things like:

• Har hun problemer med at se langt? = Does she have trouble seeing far?
• Kan hun ikke se på afstand? = Can’t she see at a distance?

But Har hun svært ved at se langt? is completely normal.

It would be:

Hun har svært ved at se langt.
= She has difficulty seeing far.

That is useful to compare with the question form:

• Hun har svært ved at se langt. = statement
• Har hun svært ved at se langt? = yes/no question

The only change is the word order: the verb moves to the front in the question.

Historically it is the same word, but in this sentence you should learn svært ved at as a set expression.

On its own, ved often means:

• by
• at
• near

Example:

• Hun står ved døren. = She is standing by the door.

But in have svært ved at, you do not need to analyze ved literally every time. It is better to remember the whole pattern:

have svært ved at + infinitive
= have difficulty doing something