Branddøren er lukket.

Because Danish usually writes compound nouns as a single word.

So:

• brand = fire
• dør = door
• branddør = fire door

Then the definite ending is added:

• branddør = a fire door
• branddøren = the fire door

This is very normal in Danish, and much more common than writing the parts separately.

In Danish, the is often attached to the end of the noun instead of standing in front of it.

Here:

• dør = door
• døren = the door

So:

• branddør = a fire door
• branddøren = the fire door

This is called the postposed definite article.

Because dør is a common gender noun in Danish.

Danish has two grammatical genders:

• common gender: usually takes en in the indefinite form and -en in the definite form
• neuter gender: usually takes et in the indefinite form and -et in the definite form

So:

• en dør → døren
• et vindue → vinduet

Since dør is common gender, branddøren is the correct form.

Because Danish main clauses normally follow the verb-second pattern, often called V2.

In a simple statement, the finite verb usually comes in position 2:

• Branddøren = first element
• er = second element

So Branddøren er lukket has the normal Danish word order for a statement.

It is the past participle of lukke (to close), but in this sentence it functions very much like an adjective.

So er lukket means the door is in a closed state.

You can think of it as similar to English is closed. It does not mainly focus on the action of closing; it describes the result or condition.

Usually it means is closed, meaning the door is already in that state.

So Branddøren er lukket normally describes a condition, not an ongoing action.

If you wanted to emphasize the action is being closed, Danish would more naturally use something like:

• Branddøren bliver lukket

That said, context matters, but in everyday use er lukket is most naturally understood as a state.

Because the noun is singular.

With this participle/adjective, Danish often shows number agreement like this:

• singular: lukket
• plural: lukkede

For example:

• Døren er lukket = the door is closed
• Dørene er lukkede = the doors are closed

Since branddøren is one door, lukket is correct.

Yes. Branddøren is the subject, er is the finite verb, and lukket is the complement describing the subject.

A simple breakdown is:

• Branddøren = subject
• er = verb
• lukket = subject complement / predicative adjective-like form

So the sentence structure is very straightforward.

The plural would be:

• Branddørene er lukkede.

Changes:

• branddøren → branddørene = the fire doors
• lukket → lukkede = closed, plural form

This is a useful pattern to remember:

• singular: Døren er lukket
• plural: Dørene er lukkede

No. In modern Danish, common nouns are not capitalized just because they are nouns.

So in the middle of a sentence you would write:

• branddøren er lukket

It is only capitalized here because it is the first word of the sentence:

• Branddøren er lukket.

The hardest part for many English speakers is ø in dør. It is a rounded vowel that English does not really have.

A few helpful points:

• brand sounds roughly like bran(d), though the Danish r is different from most English r sounds
• dør has that special ø vowel
• -en at the end is the definite ending

So the main thing to notice is that branddøren is made of:

• brand
• dør
• -en

If you are practicing pronunciation, focus especially on the vowel in dør, since that is usually the trickiest part.