Det er et virkeligt problem, hvis døren ikke kan åbnes.

Here Det er works like English It is.

Danish very often uses det er to introduce a general statement or evaluation:

• Det er godt = It is good
• Det er et problem = It is a problem

So in this sentence, det does not point to a specific thing in a very concrete way. It simply introduces the statement: It is a real problem...

Because problem is a neuter noun in Danish.

Danish nouns are mainly either:

• common gender: take en
• neuter: take et

So:

• et problem = a problem

This gender also affects the adjective, which is why you get et virkeligt problem.

Because virkelig is agreeing with the neuter noun problem.

In Danish, an adjective usually adds -t when it modifies a singular indefinite neuter noun.

So:

• en virkelig udfordring = a real challenge
• et virkeligt problem = a real problem

That -t is there because of et problem.

Here it means real.

In this sentence, virkeligt is an adjective describing the noun problem:

• et virkeligt problem = a real problem

This is different from virkelig used as an adverb, meaning really:

• et virkelig stort problem = a really big problem

So compare:

• et virkeligt problem = a real problem
• et virkelig stort problem = a really big problem

That is a very useful distinction.

Here hvis is correct because it means if in a condition:

• hvis døren ikke kan åbnes = if the door cannot be opened

Om is usually used for whether in indirect questions, not for this kind of condition:

• Jeg ved ikke, om døren kan åbnes = I do not know whether the door can be opened

So:

• hvis = if, in a conditional sense
• om = whether

Because hvis døren ikke kan åbnes is a subordinate clause.

A subordinate clause introduced by words like hvis, at, fordi, som is often separated by a comma in Danish.

So the sentence is divided into:

• Det er et virkeligt problem
• hvis døren ikke kan åbnes

You may also see the comma omitted, depending on the comma style being used, but the version with the comma is completely normal.

Because this is a subordinate clause after hvis.

In Danish, subordinate clauses usually place the negation ikke before the finite verb:

• hvis døren ikke kan åbnes

But in a normal main clause, the finite verb comes earlier, and ikke usually comes after it:

• Døren kan ikke åbnes

So this is a very important contrast:

• Main clause: Døren kan ikke åbnes
• Subordinate clause: hvis døren ikke kan åbnes

Yes. Åbnes is a passive form.

• åbne = to open
• åbnes = to be opened

So:

• Døren kan ikke åbnes = The door cannot be opened

This is different from an active sentence like:

• Han kan ikke åbne døren = He cannot open the door

Danish often forms the passive with -s, especially in concise statements like this. You could also say:

• Døren kan ikke blive åbnet

That also means The door cannot be opened, but kan ikke åbnes is shorter and very natural.

Because døren means the door, the definite form.

The sentence is talking about a specific door, or at least a door that is understood from the situation.

• en dør = a door
• døren = the door

So:

• hvis døren ikke kan åbnes = if the door cannot be opened

If you said hvis en dør ikke kan åbnes, that would sound more like if a door cannot be opened, which is more general and less tied to a specific situation.

Yes, absolutely.

You can say:

• Hvis døren ikke kan åbnes, er det et virkeligt problem.

That means the same thing.

When the hvis clause comes first, the main clause changes word order in the usual Danish way:

• er det
• not det er

That happens because Danish main clauses normally follow the verb-second pattern.

So both are correct:

• Det er et virkeligt problem, hvis døren ikke kan åbnes.
• Hvis døren ikke kan åbnes, er det et virkeligt problem.