Hun mater katten og gir den fôr og en godbit.

Because this is a complete statement in the present tense.

• å mate = to feed (infinitive)
• mater = feeds / is feeding
• å gi = to give
• gir = gives / is giving

In Norwegian, the present tense is often made by adding -r to the verb:

• å mate → mater
• å gi → gir

So Hun mater katten og gir den fôr og en godbit means She feeds the cat and gives it food and a treat.

Katten is the definite form of katt.

• katt = cat
• en katt = a cat
• katten = the cat

Norwegian usually adds the definite article to the end of the noun:

• en bil → bilen
• en hund → hunden
• en katt → katten

So mater katten means feeds the cat, not just feeds cat or feeds a cat.

Because katt is a grammatical common-gender noun in Norwegian, and the matching pronoun is often den when referring back to it.

• en katt → katten → den

So:

• Hun mater katten og gir den fôr
  = She feeds the cat and gives it food

Even though a cat is biologically male or female, Norwegian often uses den for animals unless the sex is important or the animal is being treated more personally.

You may also hear people use han or hun for pets, especially if they know the animal well:

• Hun mater katten og gir ham fôr
• Hun mater katten og gir henne fôr

But den is completely normal here.

In this sentence, den most naturally refers to katten.

That is because:

• katten is the nearest suitable noun
• it makes sense to give the cat food and a treat

So the structure is:

• Hun mater katten = She feeds the cat
• og gir den fôr og en godbit = and gives it food and a treat

Because Norwegian, like English, usually does not repeat the subject when two verbs share the same subject and are connected by og (and).

So:

• Hun mater katten og gir den fôr
  = She feeds the cat and gives it food

This is just like English:

• She feeds the cat and gives it food not usually
• She feeds the cat and she gives it food

You can repeat hun for emphasis or clarity, but it is not necessary here.

Both relate to food, but they are used differently.

• mat = food in a general sense, especially food for people
• fôr = feed / animal food

Since the sentence is about a cat, fôr is the natural word.

Examples:

• Jeg lager mat. = I make food.
• Hun kjøper kattefôr. = She buys cat food.

So gir den fôr specifically means giving the animal food suitable for animals.

Here fôr is being used as an uncountable mass noun, like food in English.

So:

• gir den fôr = gives it food

You usually do not need an article with a mass noun when speaking generally.

Compare:

• Hun gir den fôr. = She gives it food.
• Hun gir den et fôr. would sound unnatural in this meaning.

Also, fôr is a neuter noun when used countably in some contexts, but in everyday use for animal feed, it is very often treated as a mass noun with no article.

En godbit means a treat or a tidbit.

It has en because it is:

• a countable noun
• in the indefinite singular
• a common-gender noun

So:

• en godbit = a treat
• godbiten = the treat
• godbiter = treats

This contrasts with fôr, which is used here as an uncountable noun.

Because Norwegian normally follows a pattern like:

subject + verb + indirect object/direct object + other elements

Here, after gir, the pronoun den comes before the things being given:

• gir den fôr og en godbit

This is similar to English:

• gives it food and a treat

The pronoun recipient often comes early in Norwegian:

• Jeg gir ham boka. = I give him the book.
• Hun sender meg en melding. = She sends me a message.

So den comes before fôr og en godbit because it is the receiver.

Yes, that is grammatically correct.

Repeating katten is possible, but using den sounds more natural because it avoids repeating the noun.

Compare:

• Hun mater katten og gir den fôr og en godbit.
  More natural, smoother.

• Hun mater katten og gir katten fôr og en godbit.
  Also correct, but a little more repetitive.

Learners often overuse repeated nouns, while native speakers usually switch to a pronoun when the reference is already clear.

Because gi usually takes its objects directly, without a preposition.

So Norwegian says:

• gi noen noe = give someone something

In this sentence:

• den = someone/something receiving
• fôr og en godbit = what is given

So:

• gir den fôr og en godbit

Similarly:

• Jeg gir barnet en bok. = I give the child a book.
• Hun gir hunden vann. = She gives the dog water.

You do not normally say gir til den here.

The circumflex in fôr helps distinguish it from for, which is a very common word meaning things like for, too, or used in other functions depending on context.

So:

• fôr = feed, animal food
• for = for / too / because (depending on usage)

In modern writing, you may sometimes see spelling variation in some contexts, but fôr is still very useful because it clearly marks the meaning.

The vowel is pronounced long, roughly like a long o sound, though the exact pronunciation depends on dialect.

It can be either, depending on context.

Norwegian present tense often covers both:

• She feeds the cat and gives it food and a treat
  = habitual / general description
• She is feeding the cat and giving it food and a treat
  = happening now

Norwegian very often uses the simple present where English might use either simple present or present progressive.

So without more context, Hun mater katten og gir den fôr og en godbit can mean both.