Det er uhøfligt at afbryde andre, og min søster siger, at det virker stædigt ikke at lytte.

Danish very often uses det as a formal or dummy subject in this kind of sentence, just like English uses it in It is rude to interrupt others.

So:

• Det er uhøfligt at afbryde andre
• literally follows the same pattern as It is rude to interrupt others

The real idea being judged is at afbryde andre.

You can also say:

• At afbryde andre er uhøfligt

That is grammatical, but the det version usually sounds more natural in everyday Danish.

They are in the neuter singular form of the adjective.

In Danish, adjectives often take -t when they go with a neuter word such as det, especially in patterns like:

• Det er vigtigt
• Det er svært
• Det virker mærkeligt

So here:

• uhøflig → uhøfligt
• stædig → stædigt

This is why the sentence has:

• Det er uhøfligt ...
• det virker stædigt ...

Compare:

• en uhøflig person
• et uhøfligt svar

and

• en stædig elev
• det virker stædigt

No. At has two different jobs here.

1. Infinitive marker = to

In:

• at afbryde
• at lytte

at means the same kind of to as in to interrupt and to listen.

2. Conjunction = that

In:

• min søster siger, at ...

at means that.

So in this sentence, you have both:

• at = to
• at = that

That is completely normal in Danish.

The infinitives at afbryde andre and ikke at lytte express a general action or behavior. The subject is not a specific person.

It works like English:

• It is rude to interrupt others
• It seems stubborn not to listen

In both languages, this usually means people in general, someone, or you in a general sense, not one named person.

So the sentence is making a general statement about behavior.

Andre means others or other people here.

It can stand on its own as a pronoun, so Danish does not need to say andre mennesker every time.

So:

• afbryde andre = interrupt others / interrupt other people

You could say andre mennesker, but it is not necessary.

Not in this sentence.

The verb virke can mean different things depending on context. Here it means:

• seems
• appears
• comes across as

So:

• det virker stædigt = it seems stubborn / it comes across as stubborn

This is a very common use of virke in Danish.

Because lytte means listen, while høre means hear.

The difference is similar to English:

• høre = hear, perceive sound
• lytte = listen, pay attention actively

In this sentence, the idea is about not paying attention to what someone says, so lytte is the right choice.

Examples:

• Jeg kan høre musik = I can hear music
• Jeg lytter til musik = I am listening to music

When Danish negates an infinitive phrase, ikke often comes before at + infinitive.

So:

• ikke at lytte = not to listen
• ikke at forstå = not to understand
• ikke at vide = not to know

That is why the sentence has:

• det virker stædigt ikke at lytte

Here, the whole action to listen is being negated.

This is different from a finite clause, where ikke is placed differently, for example:

• at han ikke lytter = that he is not listening

The sentence has two main parts:

1. Main clause

• min søster siger

This is straightforward: subject min søster + finite verb siger.

2. Subordinate clause after at

• at det virker stædigt ikke at lytte

After the conjunction at, Danish uses subordinate-clause word order. In this clause:

• det = subject
• virker = finite verb
• stædigt = complement
• ikke at lytte = infinitive phrase

So the whole second part means something like:

• that it seems stubborn not to listen

It does not refer to a specific noun. It is another formal/dummy subject.

In:

• at det virker stædigt ikke at lytte

the real idea is the action ikke at lytte. The det is there because Danish often prefers this structure when commenting on an action or situation.

English does the same thing:

• It seems rude not to listen
• It seems stubborn not to listen

So the second det is not pointing to some object; it is part of the sentence structure.

There are two different comma situations here.

1. Before og

The comma before og separates two coordinated main clauses:

• Det er uhøfligt at afbryde andre
• og min søster siger ...

2. Before at det virker ...

The comma before at marks the start of a subordinate clause.

In modern Danish, the comma before a subordinate clause is often optional, depending on whether the writer uses start comma. So both of these may be seen:

• min søster siger, at det virker ...
• min søster siger at det virker ...

Your sentence uses the version with the extra comma.

Here it is best understood as stubborn in the sense of seeming stubborn.

Because it follows virker, it is evaluating the behavior:

• det virker stædigt ikke at lytte
• roughly: not listening seems stubborn

So stædigt is not mainly describing how someone listens. It is describing how the action of not listening appears to other people.

Almost, yes:

• Det = it
• er = is
• uhøfligt = rude / impolite
• at afbryde = to interrupt
• andre = others

So the structure is very close to English:

• It is rude to interrupt others

This is one reason this sentence is fairly learner-friendly: the overall pattern matches English quite well, even though some details, like adjective endings and ikke placement, are different.