Påstanden er feil.

Because påstanden is the definite singular form of påstand.

• en påstand = a claim / an assertion
• påstanden = the claim / the assertion

In Norwegian, definiteness is often shown by adding an ending to the noun instead of using a separate word like the in English.

So:

• En påstand er feil = A claim is wrong
• Påstanden er feil = The claim is wrong

Yes. Påstand is usually treated as a masculine noun, so it takes:

• en påstand = a claim
• påstanden = the claim

In Bokmål, many masculine nouns follow this pattern:

• en bil → bilen
• en lærer → læreren
• en påstand → påstanden

Here feil is being used like an adjective, meaning wrong / incorrect.

So:

• Påstanden er feil = The claim is wrong

If you said feilen, that would be the definite noun form the mistake / the error, which would usually not fit this sentence.

Compare:

• Påstanden er feil = The claim is wrong
• Feilen er stor = The mistake is big

So in your sentence, feil describes påstanden, rather than naming a specific error.

It is functioning as an adjective here.

That is useful to know because feil can be both:

• noun: en feil = a mistake / an error
• adjective: feil = wrong / incorrect

Examples:

• Det er en feil. = It is a mistake.
  Here feil is a noun.
• Svaret er feil. = The answer is wrong.
  Here feil is an adjective.

In Påstanden er feil, it clearly means wrong, so it is adjectival.

Some Norwegian adjectives do change form, but feil is often used in a form that stays the same in many common contexts.

For example:

• Påstanden er feil = The claim is wrong
• Svaret er feil = The answer is wrong

You may also see forms like feilt in some contexts, but in everyday modern Norwegian, feil is very commonly used unchanged, especially in predicate position after er.

For a learner, the safest pattern to remember is:

• X er feil = X is wrong

No, this is normal Norwegian statement word order:

• Påstanden = subject
• er = verb
• feil = complement

So the structure is:

Subject + verb + complement

That is the same basic pattern as English:

• The claim is wrong.

If this were a question, the verb would usually come before the subject:

• Er påstanden feil? = Is the claim wrong?

Er is the present tense of å være, which means to be.

So:

• jeg er = I am
• du er = you are
• påstanden er feil = the claim is wrong

Norwegian uses er for all persons in the present tense, unlike English, which changes between am / is / are.

Yes, but the tone and usage can differ slightly.

• Påstanden er feil = the most straightforward, common way to say The claim is wrong
• Påstanden er gal = The claim is mistaken / wrong, but gal can also mean crazy in other contexts
• Påstanden er uriktig = The claim is incorrect, a bit more formal

So feil is a very natural and common choice here.

A rough guide for an English speaker:

• Påstanden ≈ POH-stan-den
• er ≈ a short air / ehr
• feil ≈ close to fale, but as one syllable-like diphthong

A few helpful pronunciation notes:

• å in på- is a deep vowel, somewhat like the vowel in British law
• stand has a clear a
• ei in feil is a diphthong, somewhat like the vowel in day, though not exactly the same

A natural rhythm would be:

PÅstanden er FEIL

with stress especially noticeable on PÅ and feil.

Yes. Depending on context, påstand can be translated as:

• claim
• assertion
• statement

And feil can mean:

• wrong
• incorrect
• sometimes effectively false, depending on context

So Påstanden er feil could be understood as:

• The claim is wrong
• The assertion is incorrect
• The statement is false

The exact English choice depends on the situation.

Yes, very easily. This is a common Norwegian sentence pattern:

[definite noun] + er + feil

Examples:

• Svaret er feil. = The answer is wrong.
• Adressen er feil. = The address is wrong.
• Navnet er feil. = The name is wrong.
• Informasjonen er feil. = The information is wrong.

So Påstanden er feil is a very useful model sentence.