Hun skriver svaret i chatten, fordi hendes mikrofon ikke virker.

Because Danish usually adds the definite article to the end of the noun.

• svar = answer

• svaret = the answer

• chat = chat
• chatten = the chat

So English the is often shown in Danish as an ending rather than as a separate word.

That depends on the noun’s gender.

• et svar → svaret
• en chat → chatten

Danish has two grammatical genders in the singular:

• common gender nouns usually take -en in the definite singular
• neuter nouns usually take -et in the definite singular

So svar is a neuter noun, while chat is a common-gender noun.

Because sin/sit/sine can only refer back to the subject of the same clause.

In this sentence, hun is the subject of the main clause:

• Hun skriver svaret i chatten

But fordi hendes mikrofon ikke virker is a new clause. Inside that clause, hun is not the grammatical subject, so Danish uses hendes, not sin.

A useful comparison:

• Hun kan ikke finde sin mikrofon. = She cannot find her own microphone.
  Here sin refers back to hun in the same clause.

But in your sentence, the possession is inside a different clause, so hendes is correct.

Because fordi introduces a subordinate clause, and subordinate clauses in Danish have different word order from main clauses.

Compare:

• Main clause: Hendes mikrofon virker ikke.
• Subordinate clause: fordi hendes mikrofon ikke virker

In a main clause, the finite verb usually comes before ikke.
In a subordinate clause, ikke usually comes before the finite verb.

This is one of the most important Danish word-order patterns to learn.

Here virker means works, functions, or is working.

So hendes mikrofon ikke virker means that her microphone is not functioning properly.

The verb virke can also mean things like seem or have an effect, but in this sentence it clearly means work/function.

Literally, skriver means writes. But in the context of i chatten, it naturally means something like:

• types
• writes
• posts a written reply

So a natural English understanding is that she is typing the answer into the chat.

Yes, very likely.

Danish often uses the simple present where English would use the present progressive.

So:

• Hun skriver svaret i chatten
  can naturally mean
• She is writing/typing the answer in the chat

And:

• hendes mikrofon ikke virker
  can mean
• her microphone isn’t working

So the Danish present tense often covers both English simple present and present progressive, depending on context.

Because i chatten is the normal way to say that something is written inside the chat conversation.

• i chatten = in the chat

This focuses on the message appearing within the chat itself.
You may see på with websites, platforms, or apps in other contexts, but for a message written inside a chat, i chatten is the natural choice.

Yes.

You can say:

• Fordi hendes mikrofon ikke virker, skriver hun svaret i chatten.

That means the same thing.

Notice what happens in the main clause after the initial fordi-clause:

• skriver hun

This is because Danish main clauses follow the verb-second rule: the finite verb comes in second position.

It depends on which accepted Danish comma style you use.

With start comma, you write:

• Hun skriver svaret i chatten, fordi hendes mikrofon ikke virker.

Without start comma, you can write:

• Hun skriver svaret i chatten fordi hendes mikrofon ikke virker.

Both styles are accepted in modern Danish. The important thing is to be consistent within the same text.

Because Danish main clauses normally follow the verb-second pattern.

In this sentence:

• Hun = first element
• skriver = finite verb in second position
• svaret = object
• i chatten = adverbial phrase

So the neutral word order is:

• Hun skriver svaret i chatten

You can move parts around for emphasis, but then the verb still has to stay in second position in the main clause. For example:

• I chatten skriver hun svaret.

That is possible, but it sounds more marked or emphatic than the original sentence.