Door een fout begon de sleuteloverdracht later.

Here door means because of or as a result of, not physical through.

In Dutch, door can introduce a cause:

• Door de regen bleef ik thuis. = Because of the rain, I stayed home.
• Door een fout begon de sleuteloverdracht later. = Because of an error, the key handover started later.

So although door often literally means through, in sentences like this it commonly expresses cause.

Een fout means an error / a mistake in a general, non-specific way.

• een fout = an error, some error
• de fout = the error, a specific error already known from context

In this sentence, the speaker is just saying that there was some mistake, not necessarily one already identified for the listener. That is why een fout is natural here.

Begon is the past tense singular of beginnen (to begin / to start).

The subject is de sleuteloverdracht, which is singular, so the verb must also be singular in the past tense:

• ik begon
• jij begon / begon jij
• hij/zij/het begon
• de sleuteloverdracht begon

So begon means began or started.

This is a very common Dutch word-order pattern.

The sentence starts with Door een fout, which is an adverbial phrase. In a main clause, Dutch normally puts the finite verb in the second position. Because Door een fout is in first position, the verb begon must come next.

That causes inversion:

• normal order: De sleuteloverdracht begon later.
• with an opening phrase: Door een fout begon de sleuteloverdracht later.

So this is completely normal Dutch word order.

Sleuteloverdracht is a compound noun:

• sleutel = key
• overdracht = transfer, handover

Together, sleuteloverdracht means key handover or handover of the keys.

This is the kind of noun you often see in housing or real-estate contexts, for example when someone receives the keys to a house, apartment, or office.

Dutch forms compound nouns very freely, much more often than English.

Because Dutch normally writes compound nouns as one word.

So where English often has:

• key handover
• train station
• city center

Dutch often has:

• sleuteloverdracht
• treinstation
• stadscentrum

This is one of the most important spelling habits to get used to in Dutch.

Later means later in time.

In this sentence, it means the handover started later than expected / later than planned.

Dutch often puts time-related adverbs like later toward the end of the clause, especially when they modify the whole event:

• De vergadering begon later.
• Door een fout begon de sleuteloverdracht later.

So its position here is very natural.

Yes, absolutely.

• Door een fout begon de sleuteloverdracht later.
• Vanwege een fout begon de sleuteloverdracht later.

Both mean because of an error.

A small nuance:

• door is very common and natural in everyday Dutch
• vanwege can sound a bit more formal or explicit

In many contexts, either one works.

More or less, yes.

You could also say:

• Door een fout startte de sleuteloverdracht later.

Both begon and startte can mean started.
However:

• beginnen / begon is very common and neutral
• starten / startte can sometimes sound slightly more modern, technical, or process-oriented

In this sentence, begon is probably the most natural everyday choice.

In Dutch, every noun has a grammatical article: de or het.

Overdracht is a de-word, so the compound sleuteloverdracht is also a de-word.

A useful rule for compounds is:

The last part usually determines the gender/article.

Since:

• de overdracht

you get:

• de sleuteloverdracht

Yes, that is grammatically possible.

• Door een fout begon de sleuteloverdracht later.
• De sleuteloverdracht begon later door een fout.

Both are understandable. The difference is mainly emphasis:

• Door een fout ... puts the cause first, so it gets more attention.
• De sleuteloverdracht begon later ... starts with the event itself and adds the cause later.

Dutch often moves elements to the beginning of the sentence to highlight them.