Hun spiller sin rolle så godt, at hun får stor applaus fra hele salen.

Because sin is the reflexive possessive form, used when the possessor is the subject of the clause.

In Hun spiller sin rolle, the subject is hun, and the role belongs to her, so Danish uses sin.

• Hun spiller sin rolle = She plays her own role.
• Hun spiller hendes rolle would normally mean she plays another woman’s role.

This is a very important difference in Danish:

• sin/sit/sine = the subject’s own
• hans/hendes/deres = someone else’s

Because sin/sit/sine must agree with the noun being possessed, not with the owner.

The noun here is rolle, which is a common-gender singular noun: en rolle.

So you use:

• sin with common-gender singular nouns
• sit with neuter singular nouns
• sine with plural nouns

Examples:

• sin rolle = her own role
• sit hus = her own house
• sine bøger = her own books

Så ... at means so ... that.

So:

• så godt, at hun får stor applaus = so well that she receives great applause

This is a very common Danish pattern:

• Han var så træt, at han faldt i søvn. = He was so tired that he fell asleep.
• Det var så svært, at jeg gav op. = It was so difficult that I gave up.

Because godt is being used as an adverb here, meaning well, not as an adjective meaning good.

Compare:

• en god skuespiller = a good actor
• hun spiller godt = she plays well

In this sentence, godt describes how she plays, so it must be the adverb form.

Yes, it is similar. Spille can mean several things in Danish, depending on context, including:

• to play a game
• to play an instrument
• to act / play a role

Here, Hun spiller sin rolle means She plays her role or She acts her part.

So spille is a broad verb, much like English play.

This is normal Danish main-clause word order.

Danish usually follows the V2 rule, which means the finite verb comes in the second position in a main clause.

Here:

• Hun = subject
• spiller = finite verb
• sin rolle = object
• så godt = adverbial phrase

So the sentence structure is perfectly normal:

• Hun spiller sin rolle så godt ...

If another element came first, the verb would still stay in second position:

• Så godt spiller hun sin rolle, at ...

That version is possible, but it sounds more marked or literary.

Because at hun får stor applaus fra hele salen is a subordinate clause.

The comma separates the main clause from the subordinate clause:

• main clause: Hun spiller sin rolle så godt
• subordinate clause: at hun får stor applaus fra hele salen

In modern Danish, the comma before subordinate clauses is sometimes omitted, depending on the comma system being followed, so you may also see:

• Hun spiller sin rolle så godt at hun får stor applaus fra hele salen.

Both are seen, but the version with the comma is very common.

Because subordinate clauses in Danish do not follow the main-clause V2 rule.

In a subordinate clause, the subject normally comes before the finite verb:

• at hun får

Compare:

Main clause:

• Hun får stor applaus.

Subordinate clause:

• ... at hun får stor applaus.

So this is standard subordinate-clause word order in Danish.

Får literally means gets or receives.

So:

• hun får stor applaus = she gets / receives great applause

In English, receive applause may sound a little formal, while get applause is more natural in everyday speech. Danish få is often used in exactly this broad sense of get/receive.

Applaus is usually treated as an uncountable noun in Danish, much like applause in English.

So:

• stor applaus = great applause / a lot of applause

You would not normally say stor en applaus.

You may also hear:

• megen applaus = much applause
• stor applaus = great applause / strong applause

In this sentence, stor applaus sounds very natural and idiomatic.

Literally, yes: hele salen means the whole hall.

But in context, it really means everyone in the hall or the entire audience.

This is a common kind of expression in both Danish and English, where a place stands for the people in it.

So:

• fra hele salen = from the whole audience / from everyone in the hall

In Danish, hele usually comes directly before a definite noun:

• hele salen = the whole hall
• hele dagen = the whole day
• hele byen = the whole town

You do not normally say den hele sal in standard Danish for this meaning.

So hele + definite noun is the normal pattern.

Yes. Salen is the definite singular form of sal.

• en sal = a hall
• salen = the hall

Danish often makes nouns definite by adding an ending:

• en rolle → rollen
• en sal → salen

So hele salen literally means the whole hall.

Yes. Even if the meaning is already clear, there are several natural English translations, for example:

• She plays her role so well that she gets great applause from the whole audience.
• She plays her part so well that the entire audience applauds her.
• She performs her role so well that she receives loud applause from the whole hall.

The Danish sentence itself is very natural and idiomatic. The best English translation depends on whether you want to stay close to the Danish wording or sound more natural in English.

Often, yes.

Rolle means role, but in performance contexts English often also says part.

So:

• Hun spiller sin rolle can be translated as
  • She plays her role
  • She plays her part

Both work, though role is the more direct match.