Learn Hardcore Norwegian: Læreren gir henne ekstra oppmerksomhet fordi hun er modig nok til å stille vanskelige spørsmål. - The teacher gives her extra attention because she is brave enough to ask difficult questions.

Lærer means a teacher (indefinite), and læreren means the teacher (definite).
Norwegian very often uses the definite form when you are talking about a specific person that both speaker and listener can identify (for example, the regular teacher of a class).

If you said En lærer gir henne ekstra oppmerksomhet, it would sound like a (random) teacher gives her extra attention, not the teacher.

Why is henne used instead of hun?

Hun is the subject form (nominative), like she in English.
Henne is the object form (accusative), like her in English.

In this sentence:

Læreren = subject (the one doing the action)
gir = verb
henne = indirect object (the one receiving something)

So you must use henne, just like in English you would say The teacher gives her extra attention, not gives she extra attention.

Why is the word order gir henne ekstra oppmerksomhet and not gir ekstra oppmerksomhet henne?

With two objects, Norwegian usually places a short pronoun object before the longer noun phrase:

Læreren gir henne ekstra oppmerksomhet. (natural)
Læreren gir ekstra oppmerksomhet henne. (sounds odd)

If you want to put the pronoun after ekstra oppmerksomhet, you normally add a preposition:

Læreren gir ekstra oppmerksomhet til henne.

Both gir henne ekstra oppmerksomhet and gir ekstra oppmerksomhet til henne are fine; the first is just more compact.

Why is there no article before ekstra oppmerksomhet?

Oppmerksomhet is an uncountable (mass) noun here, like attention in English. In Norwegian, mass nouns usually do not take an article when you talk about them in a general or unspecific way:

ekstra oppmerksomhet = extra attention (in general)
den ekstra oppmerksomheten = the extra attention (a specific amount already known)

So Læreren gir henne ekstra oppmerksomhet matches English The teacher gives her extra attention, not an extra attention.

What does fordi do to the word order in the second part of the sentence?

Fordi introduces a subordinate (dependent) clause, like because in English.

In Norwegian:

Main clause word order is verb‑second: Læreren gir henne ekstra oppmerksomhet.
Subordinate clause (after fordi) has normal subject–verb order: fordi hun er modig nok til å stille vanskelige spørsmål.

So you get:
Læreren gir henne ekstra oppmerksomhet fordi hun er modig nok til å stille vanskelige spørsmål.

If you move the fordi‑clause to the front:
Fordi hun er modig nok til å stille vanskelige spørsmål, gir læreren henne ekstra oppmerksomhet.
Notice that then the main clause still has verb‑second (gir læreren).

Who does hun refer to here, the teacher or the girl getting attention?

Grammatically, hun could refer to either læreren or henne, because both are feminine possible referents.

However, the most natural understanding is that hun refers to henne (the one getting extra attention). The structure X does Y to her because she is brave enough to… in normal discourse almost always explains something about her, not about X.

So by default a Norwegian reader will understand that the girl who gets extra attention is the one who is brave enough to ask difficult questions.

Why do we say modig nok and not nok modig, like enough brave?

In this construction, nok is an adverb meaning enough, and it comes after the adjective:

modig nok = brave enough
stor nok = big enough
gammel nok = old enough

You cannot say nok modig here; that would be wrong in standard Norwegian.

Note: English and Norwegian match here: English also says brave enough, not enough brave.

I know nok can also mean something like probably. What does it mean here?

Nok has (at least) two common uses:

Nok = enough (degree):
- Hun er modig nok til å stille spørsmål.
  = She is brave enough to ask questions.
Nok = probably / I suppose / I guess (modal particle):
- Han kommer nok i morgen.
  = He will probably come tomorrow / I guess he will come tomorrow.

In hun er modig nok til å stille vanskelige spørsmål, nok clearly has the enough meaning, because it is directly after the adjective and followed by til å + infinitive.

Why do we need til å before stille?

This is a very typical pattern in Norwegian:

adjective (+ nok) + til å + infinitive

Examples:

modig nok til å stille spørsmål = brave enough to ask questions
sterk nok til å løfte den = strong enough to lift it
gammel nok til å kjøre bil = old enough to drive a car

After nok (and many adjectives expressing ability/sufficiency), Norwegian uses til å before the infinitive.
Saying modig nok å stille without til would be ungrammatical in standard Norwegian.

What is the difference between stille spørsmål and spørre?

Both are about asking, but they are used differently:

stille (et) spørsmål = literally to pose/ask a question
- Hun liker å stille vanskelige spørsmål.
  = She likes to ask difficult questions.
spørre = to ask (someone, about something)
- Hun liker å spørre læreren om vanskelige ting.
  = She likes to ask the teacher about difficult things.

In this sentence, stille vanskelige spørsmål focuses on the questions themselves.
If you used spørre, you would usually say spørre læreren om noe rather than spørre vanskelige spørsmål (that last one is wrong).

Why is it vanskelige spørsmål and not vanskelig spørsmål?

Because spørsmål is plural here (questions, not just one question).

In the indefinite plural, adjectives take -e, regardless of gender:

et vanskelig spørsmål = a difficult question (singular, neuter)
vanskelige spørsmål = difficult questions (plural)

Other examples:

en stor bil → store biler
et nytt ord → nye ord

Even though spørsmål looks the same in singular and plural, the adjective shows that it is plural in this sentence: vanskelige spørsmål.

Could we say Læreren gir henne ekstra mye oppmerksomhet instead? Does it mean the same?

You can say ekstra mye oppmerksomhet, and it is grammatical.

The nuance:

ekstra oppmerksomhet = more attention than normal, some extra
ekstra mye oppmerksomhet = a lot of extra attention, it emphasizes the amount more strongly

So the original sentence is neutral: the teacher gives her some extra attention, more than usual.
With ekstra mye, you picture noticeably large amounts of attention.

Can I say fordi at hun er modig nok til å stille vanskelige spørsmål, or is fordi at wrong?

In everyday spoken Norwegian, many people say fordi at, and it is widely used.

However, in standard written Bokmål, fordi alone is usually preferred and sounds more formal and correct:

Recommended in writing: fordi hun er modig nok …
Colloquial / dialectal: fordi at hun er modig nok …

As a learner aiming at standard, use fordi without at in writing; you will often hear fordi at in speech.

How do you pronounce æ in Læreren?

The letter æ is usually pronounced like the vowel in English cat or bad, but often a bit longer and clearer.

In Læreren:

Læ- sounds roughly like lae in lad but with a slightly longer vowel: [læː].

So Læreren is approximately [ˈlæːrərə(n)] in many accents, with the stress on the first syllable.