Foreldrepengesøknaden er klar.

It is a compound noun, which is very common in Norwegian.

It is made up of:

• foreldre = parents / parental
• penger = money
• søknad = application

Together, foreldrepengesøknad means something like parental benefit application or application for parental benefits.

Then the ending -en is added, giving foreldrepengesøknaden = the parental benefit application.

Norwegian often combines ideas into one noun where English would use several words.

In Norwegian, the definite article is often added as a suffix to the noun.

So:

• en søknad = an application
• søknaden = the application

The same happens with the full compound:

• en foreldrepengesøknad = a parental benefit application
• foreldrepengesøknaden = the parental benefit application

This is one of the biggest differences from English.

Because søknad is a common gender noun in Bokmål, and the definite singular ending for many common gender nouns is -en.

Compare:

• en bil → bilen
• en søknad → søknaden

Since the whole compound takes its gender from the last part of the compound, foreldrepengesøknad is also common gender, so it becomes foreldrepengesøknaden.

Because klar must agree with the noun it describes.

Here, foreldrepengesøknaden is:

• singular
• common gender
• definite

For a predicate adjective after er, the usual forms are:

• common gender singular: klar
• neuter singular: klart
• plural: klare

So:

• Søknaden er klar. = The application is ready.
• Brevet er klart. = The letter is ready.
  (brev is neuter)
• Dokumentene er klare. = The documents are ready.

Because in this sentence, the noun is definite by itself through the ending -en.

So foreldrepengesøknaden already means the parental benefit application.

You would use den only in certain other structures, especially when an adjective comes before the noun:

• foreldrepengesøknaden = the parental benefit application
• den ferdige foreldrepengesøknaden = the finished parental benefit application

This is often called double definiteness in Scandinavian grammar.

Yes. Klar is an adjective, and here it is used as a predicate adjective.

In other words:

• Foreldrepengesøknaden = subject
• er = verb
• klar = adjective describing the subject

This works just like English is ready.

Compare:

• Maten er varm. = The food is warm.
• Døra er åpen. = The door is open.
• Foreldrepengesøknaden er klar. = The parental benefit application is ready.

Yes. That is a natural alternative.

Compare:

• Foreldrepengesøknaden er klar.
• Søknaden om foreldrepenger er klar.

The first version is more compact because it uses a compound noun.
The second spells the idea out with om + noun phrase: application for parental benefits.

Norwegian often allows both styles, but compounds are very common and often sound more official or administrative.

The word order is straightforward:

• Foreldrepengesøknaden = subject
• er = verb
• klar = complement/adjective

So it follows the normal Norwegian pattern:

subject + verb + complement

This is similar to English:

• The application is ready.

If something else came first in the sentence, Norwegian would still keep the verb in second position:

• Nå er foreldrepengesøknaden klar. = Now the parental benefit application is ready.

In Norwegian, common nouns are not capitalized unless they begin the sentence.

So:

• søknad
• foreldrepenger
• foreldrepengesøknaden

Only the first word here starts with a capital letter because it is at the beginning of the sentence:

• Foreldrepengesøknaden er klar.

This is normal Norwegian spelling.

The indefinite version would be:

En foreldrepengesøknad er klar.

That means a parental benefit application is ready.

Compare:

• En foreldrepengesøknad = a parental benefit application
• Foreldrepengesøknaden = the parental benefit application

So the difference is:

• en before the noun for indefinite singular
• -en attached to the noun for definite singular

Yes, this sentence is standard Bokmål.

A Nynorsk version might be:

Foreldrepengesøknaden er klar.

In this particular case, it can look the same, although vocabulary and grammar often differ between Bokmål and Nynorsk in other sentences.

So for a learner, this sentence is perfectly normal Bokmål, and it may also be understandable or even identical in Nynorsk depending on context.