Eftir sjónprófið fór hún beint í apótekið, og lyfjafræðingurinn svaraði spurningunum hennar aftur.

Because Icelandic normally follows a verb-second pattern in main clauses.

Here, the sentence starts with the time phrase Eftir sjónprófið. Once that element takes first position, the finite verb comes next:

• Eftir sjónprófið fór hún...

If you started directly with the subject, you would say:

• Hún fór beint í apótekið.

So this is not unusual word order; it is a very normal Icelandic pattern.

Here eftir means after in a time sense, and in that use it takes the accusative.

So:

• sjónpróf = a vision test / eye test
• sjónprófið = the vision test / the eye test

The ending -ið is the suffixed definite article, so the noun itself carries the meaning of the.

A learner may notice that eftir can appear with other cases in other meanings, but in this sentence the temporal meaning after gives you sjónprófið.

It is a compound noun:

• sjón = sight, vision
• próf = test, exam

So sjónpróf is literally something like vision-test.

Compounds like this are extremely common in Icelandic.

Beint is an adverb here, meaning something like straight or directly.

It comes from the adjective:

• beinn = straight, direct

A very common Icelandic pattern is that an adverb has the same form as the neuter singular of an adjective:

• beinn → beint

So hún fór beint í apótekið means she went straight/directly to the pharmacy.

Because í changes case depending on whether you mean:

• movement into/to a place → accusative
• being in a place → dative

Here she is going to the pharmacy, so it is a destination:

• í apótekið = into/to the pharmacy

Compare:

• Hún fór í apótekið. = She went to the pharmacy.
• Hún var í apótekinu. = She was in the pharmacy.

So the contrast is:

• apótekið = accusative
• apótekinu = dative

Because Icelandic makes lots of compound nouns.

This word is built from the idea of medicine/drugs plus science/study, and then a person-ending:

• lyf = medicine, drug
• lyfjafræði = pharmacy / pharmaceutical science
• lyfjafræðingur = pharmacist

Then -inn is the definite article:

• lyfjafræðingur = a pharmacist
• lyfjafræðingurinn = the pharmacist

So the whole word is completely normal Icelandic word-building, even if it looks long at first.

Because the verb svara takes the dative case.

So even though English says answer the questions, Icelandic uses dative after svara:

• spurning = question
• spurningum = to questions / questions (dative plural)
• spurningunum = the questions (dative plural definite)

So:

• svaraði spurningunum hennar

is using the correct dative form after svaraði.

This is one of those verbs whose case pattern you simply have to learn.

That is a normal Icelandic pattern.

In Icelandic, possessive pronouns often come after the noun:

• spurningunum hennar = her questions

So unlike English her questions, Icelandic very often prefers questions her in structure.

Also, hennar is the genitive form of hún, because possession after a noun is expressed with the genitive.

Because sinn is a reflexive possessive, and it normally refers back to the subject of its own clause.

In the second clause, the subject is:

• lyfjafræðingurinn

So if you said:

• spurningunum sínum

that would mean his own questions — the pharmacist’s questions.

But the questions belong to hún from the earlier clause, not to the pharmacist. So Icelandic uses the non-reflexive form:

• spurningunum hennar

That means her questions.

Aftur usually means again or back.

With svara, it can give slightly different shades depending on context, for example:

• answered again
• answered back
• replied

So this word adds an extra nuance; it is not just a meaningless filler.

Its position at the end of the clause is very natural for a short adverb in Icelandic. If you removed it, the sentence would still be grammatical, but the meaning would be a little different.