Når hun har opdateret computeren, vil hun genstarte den og prøve igen.

Yes. Når usually means when in the sense of a general or future time relationship.

In this sentence, Når hun har opdateret computeren ... means When she has updated the computer ...

A useful contrast is:

• når = when, for something that happens regularly or is expected in the future
• da = when, for a specific event in the past

So here når is correct because the sentence is about something that will happen later.

Har opdateret is the present perfect form:

• har = has
• opdateret = updated

So hun har opdateret means she has updated.

In Danish, this is often used in clauses like this to show that one action must be completed before the next one happens:

• Når hun har opdateret computeren, vil hun genstarte den ...
• When she has updated the computer, she will restart it ...

It highlights that the updating comes first, and only after that will she restart it.

Because this is a subordinate clause introduced by når.

In Danish subordinate clauses, the subject usually comes before the finite verb:

• Når hun har opdateret computeren
• when she has updated the computer

If you said Når har hun opdateret computeren?, that would sound like a question structure, roughly When has she updated the computer?

So the sentence uses normal subordinate-clause word order, not question word order.

This is because the sentence begins with a subordinate clause. After a fronted element like that, Danish uses verb-second word order in the main clause.

So:

• Når hun har opdateret computeren, ... = fronted subordinate clause
• then the main clause begins with the finite verb: vil
• then the subject: hun

That is why you get:

• Når hun har opdateret computeren, vil hun genstarte den ...

If the main clause stood alone, it would be:

• Hun vil genstarte den og prøve igen.

But once the Når-clause comes first, the main clause changes to:

• ..., vil hun genstarte den ...

Here vil means will, expressing the future.

• hun vil genstarte den = she will restart it

It is true that ville/vil can sometimes relate to willingness or intention depending on context, but in this sentence the natural reading is future time.

So the sentence means that after updating the computer, her next actions will be restarting it and trying again.

Because genstarte means restart, literally start again.

• starte = start
• genstarte = restart / reboot

The prefix gen- often gives the idea of again or re-:

• genlæse = reread
• genåbne = reopen
• genstarte = restart

So genstarte den is specifically restart it, not just start it.

Den refers back to computeren.

• computeren = the computer
• den = it

Danish nouns have grammatical gender, and computer is a common gender noun, so the pronoun used is den.

A quick overview:

• common gender noun → den
• neuter noun → det

Since computeren is common gender, the sentence uses den:

• genstarte den = restart it

Because they follow vil, which is a modal verb.

After modal verbs in Danish, the next verb is normally in the infinitive without at:

• vil genstarte
• kan prøve
• skal vente
• må gå

So:

• vil hun genstarte den og prøve igen
• she will restart it and try again

Notice that prøve is also infinitive because it is coordinated with genstarte after vil.

Because after vil, Danish does not use at before the infinitive.

Compare:

• Hun vil prøve igen. = She will try again.
• Hun vil genstarte den og prøve igen.

This is similar to English, where you also say will try, not will to try.

You do use at in many other infinitive constructions, but not after modal verbs like vil.

Igen means again.

Here:

• prøve igen = try again

Its position is natural after the infinitive verb prøve. Danish often places adverbs like this after the verb phrase they belong to.

So the final part:

• og prøve igen
• and try again

means she will make another attempt after restarting the computer.

Yes, often Danish can use the present tense for future meaning if the context is clear.

For example, Danish might also say:

• Når hun har opdateret computeren, genstarter hun den og prøver igen.

That can still mean:

• When she has updated the computer, she restarts it and tries again / she will restart it and try again.

Using vil makes the future meaning more explicit. So the version in your sentence is perfectly natural and clear.