Dómarinn flautaði og keppnin hófst strax.

Because -inn is the suffixed definite article in Icelandic, roughly equivalent to the in English.

• dómari = a judge / a referee
• dómarinn = the judge / the referee

In this sentence, the speaker is talking about a specific referee, so the definite form is used.

A useful thing to notice is that Icelandic usually attaches the to the end of the noun instead of putting it in front.

For the same reason: keppnin is the definite form.

• keppni = a competition
• keppnin = the competition

So both nouns in the sentence are definite:

• Dómarinn = the referee
• keppnin = the competition

The exact shape of the article changes depending on gender, case, and the form of the noun, so you should not expect every noun to add the article in exactly the same way.

Flautaði is the 3rd person singular past tense of flauta.

• að flauta = to whistle / blow a whistle
• hann/hún flautaði = he/she whistled

Here it matches dómarinn, which is a singular subject.

This verb is a regular weak verb, so it forms the past tense with -aði.

Hófst is the past tense, 3rd person singular of hefjast.

• að hefjast = to begin / to start
• hófst = began / started

It looks different because:

1. hefjast is not a regular verb.
2. It has a vowel change in the past tense: hefj- → hóf-
3. It includes the -st ending, which belongs to the verb itself.

A very useful distinction is:

• að hefja eitthvað = to begin something
  
  • Hann hóf leikinn = He began the game
• að hefjast = to begin / start
  
  • Leikurinn hófst = The game began

So in your sentence, keppnin hófst means the competition began, with the competition itself as the subject.

Because the verb here is hefjast, not hefja.

The -st ending is part of a common Icelandic verb pattern often called the middle voice. In many cases, verbs with -st are used where English would use an intransitive verb or a passive-like meaning.

In this sentence:

• hefja = to start something
• hefjast = to start / to begin

So keppnin hófst is not passive in the English sense, but it functions a bit like the competition got started / began.

Both are in the nominative case because they are the subjects of their clauses.

• Dómarinn flautaði
  Here dómarinn is the one doing the action.
• keppnin hófst
  Here keppnin is the thing that began.

So although the sentence has two clauses joined by og, each clause has its own subject in the nominative.

Because both clauses use a very basic main-clause pattern:

• Dómarinn flautaði
• keppnin hófst

That is simply subject + verb, which also feels natural in English.

However, Icelandic is often described as a V2 language, meaning that in main clauses the finite verb usually comes in the second position. In this sentence, the subject happens to be first, so the word order looks especially English-like.

For example, if you fronted strax, the verb would come before the subject:

• Strax hófst keppnin

That is normal Icelandic word order.

Og simply means and and joins two main clauses:

• Dómarinn flautaði
• keppnin hófst strax

So the whole sentence is a coordination of two events:

1. the referee blew the whistle
2. the competition started immediately

It does not force a special verb form here; it just links the two clauses.

Strax means immediately / right away.

In your sentence it comes at the end of the second clause:

• keppnin hófst strax

That placement is very natural. But Icelandic adverbs can often move, depending on emphasis and style. For example:

• Keppnin hófst strax
• Strax hófst keppnin

Both are possible, but the second one gives strax more emphasis and also shows the normal V2 behavior of Icelandic main clauses.

It can mean either, depending on context.

• In legal contexts, dómari usually means judge.
• In sports or competitions, it often means referee or official.

In this sentence, because the person blew a whistle and the competition then began, referee is the natural interpretation.

A few helpful pronunciation points:

• Dómarinn: stress the first syllable, as Icelandic almost always does.
• ó is a different vowel from plain o; it is pronounced more like oh with a glide.
• á is also its own vowel, not just a with stress.
• hófst may feel tricky because of the consonant cluster -fst at the end.

Very roughly for an English speaker:

• Dómarinn ≈ DOH-ma-rinn
• flautaði ≈ FLOI-ta-thi
• keppnin ≈ KHEP-nin
• hófst ≈ HOH-fst
• strax ≈ strahks

Those are only rough guides, but the most important thing to remember is that Icelandic always stresses the first syllable.