Vandskaden skyldes rørbruddet.

In this sentence, skyldes means is due to or is caused by.

A very useful pattern is:

X skyldes Y = X is due to Y

So:

• Vandskaden = the water damage
• skyldes = is due to / is caused by
• rørbruddet = the pipe burst / the pipe rupture

This means the first thing is the result/problem, and the second thing is the cause.

Because skyldes is the form used in this kind of passive-style construction.

Compare:

• skylder = owes in active use
  
  • Jeg skylder ham penge = I owe him money
• skyldes = is due to / is caused by
  
  • Problemet skyldes regnen = The problem is due to the rain

So in your sentence, Danish is not saying something like the water damage owes the pipe burst. It uses the special construction skyldes to express cause.

Yes. It is an -s passive form of skylde.

Danish often makes the passive in two ways:

• with blive
  • past participle
• with an -s ending

Here, Danish uses the -s form:

• skyldes

In practice, X skyldes Y is a very common set expression meaning X is due to Y.

Because the two nouns have different grammatical genders.

• en vandskade → vandskaden
• et rørbrud → rørbruddet

So:

• -en is the definite ending for many common gender nouns
• -et is the definite ending for many neuter nouns

The gender comes from the noun itself, so it has to be learned with the word:

• en vandskade
• et rørbrud

Because Danish usually puts the definite article at the end of the noun.

So instead of a separate word like English the, Danish often uses a suffix:

• vandskade = water damage

• vandskaden = the water damage

• rørbrud = pipe burst / pipe rupture
• rørbruddet = the pipe burst / the pipe rupture

That is completely normal Danish.

A separate article like den or det is usually added when there is an adjective:

• vandskaden = the water damage
• den alvorlige vandskade = the serious water damage

In the pattern X skyldes Y:

• X = the thing being explained
• Y = the reason or cause

So here:

• Vandskaden = the result/problem
• rørbruddet = the cause

That is why the sentence means that the water damage happened because of the pipe burst.

You can say that grammatically, but the meaning changes.

• Vandskaden skyldes rørbruddet = The water damage is due to the pipe burst
• Rørbruddet skyldes vandskaden = The pipe burst is due to the water damage

So simply swapping the nouns does not keep the same meaning.

If you want to express the same idea with the pipe burst as subject, Danish would usually use a different verb, for example:

• Rørbruddet forårsagede vandskaden = The pipe burst caused the water damage

Because Danish, like German, very often forms compound nouns as a single word.

So:

• vand
  • skade → vandskade
• rør
  • brud → rørbrud

This is very normal in Danish.

The last part is the main word:

• vandskade is a kind of skade
• rørbrud is a kind of brud

That last part also usually determines the gender:

• en skade → en vandskade
• et brud → et rørbrud

The dictionary forms are the indefinite singular forms:

• en vandskade
• et rørbrud

That is how you would normally look them up.

The sentence uses the definite singular forms:

• vandskaden
• rørbruddet

So when learning vocabulary, it is a good idea to memorize the noun together with its article:

• en vandskade
• et rørbrud

It would probably be understood, but Vandskaden skyldes rørbruddet is the more natural and idiomatic way to say it.

Danish often prefers:

• Vandskaden skyldes rørbruddet
• Vandskaden er forårsaget af rørbruddet

rather than:

• Vandskaden er på grund af rørbruddet

So if you want a clean, standard way to express cause in this kind of sentence, skyldes is an excellent choice.

The sentence is in the present tense:

• Vandskaden skyldes rørbruddet = The water damage is due to the pipe burst

The past tense is:

• Vandskaden skyldtes rørbruddet = The water damage was due to the pipe burst

So the change is:

• skyldes → skyldtes

Those are two vowels that English speakers often find difficult:

• y in skyldes
• ø in rørbruddet

A rough guide:

• y: make an ee sound while rounding your lips
• ø: a rounded front vowel with no exact English equivalent; keep your lips rounded more than you would in most English vowels

You do not need perfect pronunciation right away, but it helps to notice that both are rounded vowels, which is something English uses much less than Danish does.