Pleiepengene gjelder det syke barnet.

Because barnet is a neuter noun.

In Norwegian:

• en-words use den in this pattern
• et-words use det

Since barn is an et-word:

• indefinite: et barn
• definite: barnet

So with an adjective, you get:

• det syke barnet = the sick child

Because the noun phrase is definite.

Compare:

• et sykt barn = a sick child
• det syke barnet = the sick child

In Norwegian, adjectives usually take:

• -t with neuter singular indefinite: sykt
• -e in definite forms: syke

So even though barn is neuter, the adjective becomes syke here because the whole phrase is definite.

This is a very common Norwegian pattern called double definiteness.

When a noun is definite and has an adjective before it, Norwegian normally uses:

1. a definite article before the adjective
2. a definite ending on the noun

So:

• barnet = the child
• det syke barnet = literally something like the sick the-child

That may feel unusual to an English speaker, but it is normal Norwegian grammar.

Here, gjelder means something like:

• concerns
• applies to
• is about

So Pleiepengene gjelder det syke barnet means that the care benefit is connected specifically to the sick child.

It does not mean is valid in a time-related sense here. The exact nuance depends on context, but concerns / applies to is the best grammatical understanding.

The subject is Pleiepengene.

The sentence structure is:

• Pleiepengene = subject
• gjelder = verb
• det syke barnet = object/complement affected by the verb

So the sentence follows normal Norwegian main-clause word order: Subject + Verb + Object

It is plural in form.

The base word is pleiepenger, which is a set expression referring to this type of benefit/payment. Like several money-related words in Norwegian, it often appears in a plural-looking form.

Here:

• pleiepenger = care benefit / care allowance
• pleiepengene = the care benefit(s)

Even if the English translation uses a singular-sounding phrase like the care benefit, the Norwegian form itself is plural.

Because Norwegian verbs do not change according to the subject the way English verbs sometimes do.

In English:

• the child is
• the children are

In Norwegian, the present tense verb form stays the same:

• barnet gjelder would be ungrammatical for other reasons, but the point is the verb form itself does not change for number
• pengene gjelder
• barnet gjelder
• barna gjelder

So gjelder is the same form no matter whether the subject is singular or plural.

Usually, gjelder is used without for in this kind of sentence.

So:

• Pleiepengene gjelder det syke barnet is the more natural structure.

In some contexts, Norwegian does use gjelder for, but that often has a slightly different feel, more like applies to in a general rule-based sense. In this sentence, the direct object version is the most straightforward and idiomatic.

No, that would be incorrect.

Because the noun phrase is definite, the adjective must be in the definite form:

• det syke barnet ✅

Not:

• det sykt barnet ❌

A useful contrast is:

• et sykt barn = a sick child
• det syke barnet = the sick child

Yes. Syke here can naturally be translated as:

• sick
• ill

English choice depends on style and context. Grammatically, Norwegian syk / syke covers the basic idea of being unwell.

Because det syke barnet is just a noun phrase, not a relative clause.

It means:

• the sick child

If you wanted a longer structure like the child that is sick, Norwegian could say:

• barnet som er sykt

So compare:

• det syke barnet = the sick child
• barnet som er sykt = the child that is sick

Both can refer to the same thing, but the first is more compact and is exactly what your sentence uses.