Hun skriver en unnskyldning.

Because unnskyldning is a common-gender noun in Norwegian, so it takes en in the indefinite singular.

• en unnskyldning = an apology / an excuse
• unnskyldningen = the apology / the excuse

In Bokmål, nouns are usually either:

• common gender → en
• neuter → et

So this is something you often just have to learn with the noun: en unnskyldning.

Yes. skriver is the present tense of å skrive (to write).

A very useful pattern in Norwegian is:

• å skrive = to write
• skriver = write / writes / is writing
• skrev = wrote
• har skrevet = have/has written

So in Hun skriver en unnskyldning, skriver means writes or is writing, depending on context.

It can mean both.

Norwegian often uses the simple present where English may use either:

• She writes an apology
• She is writing an apology

The context usually tells you which is meant.

If you really want to stress the ongoing action, Norwegian can also use a construction like:

• Hun sitter og skriver en unnskyldning = She is sitting and writing an apology
• Hun holder på å skrive en unnskyldning = She is in the process of writing an apology

But in many everyday sentences, skriver is enough.

This is the difference between indefinite and definite.

• en unnskyldning = an apology
• unnskyldningen = the apology

So:

• Hun skriver en unnskyldning. = She is writing an apology.
• Hun skriver unnskyldningen. = She is writing the apology.

In Norwegian, the definite form is usually added to the end of the noun.

Yes. Unnskyldning can mean both apology and excuse, depending on context.

For example:

• Hun skylder ham en unnskyldning. = She owes him an apology.
• Det er bare en unnskyldning. = That is just an excuse.

So if you see unnskyldning, context matters.

This is the normal subject–verb–object order:

• Hun = subject
• skriver = verb
• en unnskyldning = object

So it works much like English:

• She
  • writes/is writing
    • an apology

Norwegian main clauses often look very familiar to English learners in simple statements like this.

Yes, hun is the third-person singular pronoun meaning she.

Compare:

• hun = she
• han = he
• jeg = I
• du = you

So Hun skriver means She writes / She is writing.

This word can be tricky for English speakers.

A rough guide is something like:

• UNN-shyld-ning

But that is only approximate.

A few helpful points:

• u in Norwegian is not the same as English u
• y is a rounded front vowel that English does not really have
• sk before y is pronounced like sh

So unnskyldning begins with something close to unn-sh...

If you want to sound more natural, it is best to listen to native audio and repeat it a few times, because the vowels are the hardest part.

Because this sentence is not using the infinitive.

Here you have a finite verb in the present tense:

• Hun skriver = She writes / is writing

If you wanted to write, you would use the infinitive:

• å skrive = to write

For example:

• Hun vil skrive en unnskyldning. = She wants to write an apology.

So:

• skriver = present tense
• å skrive = infinitive

Usually, yes, in sentences like this.

• en unnskyldning = an apology

But remember that en also shows the noun’s gender, which English articles do not do.

So in this sentence, en does two jobs:

1. it makes the noun indefinite
2. it shows that unnskyldning is common gender

No, that would not be wrong, but it means something a little more specific.

• Hun skriver en unnskyldning. = She is writing an apology.
• Hun skriver et unnskyldningsbrev. = She is writing a letter of apology / an apology letter.

So unnskyldning is broader, while unnskyldningsbrev specifically means an apology letter.

No. That is one of the nice things about Norwegian.

The verb form stays the same:

• Jeg skriver = I write
• Du skriver = you write
• Hun skriver = she writes
• Vi skriver = we write

Unlike English, Norwegian does not add a special -s form for he/she/it in the present tense.

So once you know skriver, you can use it with all subjects.