Hún fékk aðra óvenjulega spurningu, en svaraði henni á eðlilegan hátt.

• fékk is the past tense of fá — to get / receive
• svaraði is the past tense of svara — to answer

Both are 3rd person singular past, matching hún.

A useful contrast:

• hún fær = she gets
• hún fékk = she got
• hún svarar = she answers
• hún svaraði = she answered

Aðra is a form of annar.

In Icelandic, annar can mean:

• another
• other
• sometimes second, depending on context

Here it means another: another unusual question.

The form is aðra because it must agree with spurningu, which is feminine singular accusative.

Because the whole phrase is the direct object of fékk.

The verb fá commonly takes an accusative object, so question appears in the accusative:

• dictionary form: spurning
• here: spurningu = accusative singular

Everything in the noun phrase agrees with that noun:

• aðra = feminine singular accusative
• óvenjulega = feminine singular accusative
• spurningu = feminine singular accusative

So the endings are there because of case agreement.

Because it is agreeing with spurningu, which is feminine singular accusative, and it is in the weak adjective form.

The reason it is weak is that it follows aðra (another), which behaves like a determiner here. After words like that, Icelandic adjectives often take the weak declension.

So:

• óvenjulegur = dictionary form
• óvenjulega = weak feminine accusative singular

In Icelandic, pronouns follow the grammatical gender of the noun they refer to.

The noun spurning (question) is feminine, so when referring back to it, Icelandic uses the feminine pronoun:

• spurning → feminine
• henni = to it / it, when the noun referred to is feminine and the verb requires dative

So even though English says it, Icelandic uses a form that looks like her because the noun is grammatically feminine.

Because the verb svara takes the dative case, not the accusative.

So Icelandic says:

• svara einhverju = answer something

That gives:

• henni = to it / it in the dative
• not hana, which would be accusative

This is one of those verb patterns you simply have to learn with the verb:

• fá eitthvað = get something (accusative)
• svara einhverju = answer something (dative)

Because Icelandic can omit the repeated subject in coordinated clauses when it is clearly the same as before.

So this:

• Hún fékk ... , en svaraði ...

means the same as:

• Hún fékk ... , en hún svaraði ...

The second hún is unnecessary because the subject is obviously still the same person.

English does something similar:

• She got another question, but answered it normally.

Not in the way a subordinating conjunction would.

En means but and joins two main clauses. It does not trigger subordinate clause word order.

So the basic idea is still main-clause structure. In this sentence, the verb comes right after en simply because the repeated subject hún has been left out.

If the subject were included, you would get:

• ..., en hún svaraði henni ...

It is a very common Icelandic way to say in a ... way / manner.

Literally, háttur means way / manner, and the whole phrase means:

• á eðlilegan hátt = in a normal/natural way

So instead of using a single adverb, Icelandic often uses this kind of expression:

• á skemmtilegan hátt = in a fun way
• á undarlegan hátt = in a strange way
• á eðlilegan hátt = in a normal way

Because eðlilegan agrees with hátt, and háttur is masculine.

In this phrase:

• hátt = accusative singular of háttur
• eðlilegan = masculine accusative singular

So the adjective matches the noun:

• eðlilegur háttur = a normal way/manner
• á eðlilegan hátt = in a normal way

Unlike óvenjulega earlier in the sentence, this adjective is in the strong form, because there is no determiner like the, this, or another before it.

Grammatically, henni could mean her or it, because it is just the dative feminine singular pronoun.

So out of context, it could refer to:

• a woman
• a feminine noun like spurning

But in this sentence, the natural reference is spurningu (the question), so the meaning is answered it.

Yes. It is normal to use a comma before en when it links two independent parts of a sentence, especially when each side has its own verb:

• Hún fékk ... , en svaraði ...

So the comma here is standard and helps separate the two coordinated clauses.