Det ivrige barnet starter først.

Here, det is part of the noun phrase det ivrige barnet, which means the eager child.

In Norwegian, det can mean different things in different contexts:

• it → as a pronoun
• that → as a demonstrative
• part of a definite noun phrase → like the before a neuter noun with an adjective

In this sentence, it is best understood as part of the eager child, not as a separate it.

Yes, in a way they both contribute to definiteness. This is a normal Norwegian pattern often called double definiteness.

• barn = child
• barnet = the child
• det ivrige barnet = the eager child

When a definite noun has an adjective before it, Norwegian usually uses:

• a separate definite word: det
• plus the noun in its definite form: barnet

So:

• barnet = the child
• det ivrige barnet = the eager child

You usually cannot just say ivrige barnet in standard Bokmål.

Because barn is a neuter noun in Norwegian.

The definite words used before adjectives depend on gender:

• den for masculine/feminine nouns
• det for neuter nouns
• de for plural

Since barn is neuter:

• et barn = a child
• barnet = the child
• det ivrige barnet = the eager child

If it were a masculine noun, you would expect den instead.

Because the adjective is used in a definite noun phrase.

Compare:

• et ivrig barn = an eager child
• det ivrige barnet = the eager child

In Norwegian Bokmål, adjectives usually take the -e form when they come before a noun that is definite. So:

• indefinite: ivrig
• definite: ivrige

That is why you get det ivrige barnet.

Barnet is the definite singular form of barn.

• barn = child
• et barn = a child
• barnet = the child

The noun barn is neuter, so its indefinite article is et, and the definite singular ending is -et.

So:

• base noun: barn
• definite singular: barnet

Starter is the present tense of the verb å starte.

So:

• å starte = to start
• starter = starts / is starting

In Norwegian, the present tense is the same for all persons:

• jeg starter = I start
• du starter = you start
• barnet starter = the child starts

Unlike English, the verb does not change depending on the subject.

Først here means first in the sense of before the others or in first place in order.

So:

• Det ivrige barnet starter først.
• The eager child starts first.

It is an adverb, modifying the verb starter.

This is a very common question.

• først = first as an adverb
• første = first as an adjective/ordinal

Examples:

• Han kom først. = He arrived first.
• Den første dagen = The first day

In your sentence, we need the adverb, because it describes how/when the child starts, so først is correct.

Yes. This is standard Norwegian main-clause word order:

• Det ivrige barnet = subject
• starter = verb
• først = adverb

So the structure is:

Subject + Verb + Adverb

That is a very normal pattern in Norwegian.

Yes. That means The child starts first.

The adjective ivrige just adds extra information:

• Barnet starter først. = The child starts first.
• Det ivrige barnet starter først. = The eager child starts first.

But if you want to include the adjective in a definite phrase, you normally need the full form:

• det ivrige barnet

not just:

• ivrige barnet

Sometimes Norwegian definite forms can feel a little like English that, depending on context and emphasis. But in a neutral sentence like this, the most natural reading is simply:

the eager child

If you wanted a clearer demonstrative meaning, Norwegian would often use extra emphasis or context.

So for a learner, the safest interpretation here is:

• det ivrige barnet = the eager child

Yes, this is standard Bokmål.

Everything in the sentence is normal Bokmål:

• det
• ivrige
• barnet
• starter
• først

A Norwegian learner would be perfectly safe treating this as a standard Bokmål sentence.