Eftir rifrildið fór hún út að ganga í smástund og kom síðan rólegri heim.

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

The noun is rifrildi = argument / quarrel.
Rifrildið is the definite singular form, meaning the argument.

So:

• rifrildi = an argument
• rifrildið = the argument

Because rifrildi is a neuter noun, the nominative and accusative singular look the same, so you do not see a visible case change here.

Both are possible, but Icelandic often puts a time phrase first for emphasis or flow.

When a phrase like Eftir rifrildið comes first, Icelandic follows its usual verb-second pattern. That means the finite verb comes next:

• Eftir rifrildið fór hún...

Not:

• Eftir rifrildið hún fór...

So the order is:

1. Eftir rifrildið = after the argument
2. fór = went
3. hún = she

This is a very common Icelandic word-order pattern.

Literally, fór hún út að ganga is something like:

• she went out to walk

But in natural English it usually means:

• she went out for a walk

The að + infinitive construction often shows purpose after verbs of motion such as fara.

So:

• fara út að ganga = to go out to walk / to go out for a walk

This is a very natural Icelandic expression.

Yes. Ganga basically means to walk.

In this sentence, it is not just the physical act of walking in a neutral sense; together with fara út að ganga, it forms a common expression meaning to go out for a walk.

So even though ganga on its own means walk, the whole phrase is best understood as one unit.

Í smástund means for a short while or for a little while.

• smástund = a short while / a brief moment

Icelandic often uses í with expressions of duration:

• í smástund = for a short while
• í tvo daga = for two days
• í langan tíma = for a long time

So here í does not mean in in a literal location sense. It is part of a time expression meaning for.

Rólegri is the comparative form of rólegur, which means calm.

So:

• róleg = calm
• rólegri = calmer

The idea is that she came home calmer than before. Icelandic often uses the comparative without explicitly stating than before if the meaning is obvious from context.

So:

• kom rólegri heim = came home calmer

This is a very natural way to describe a change of state.

Because heim is an adverb meaning homeward / home when there is motion toward home.

Compare:

• fara heim = go home
• koma heim = come home

But:

• vera heima = be at home

So Icelandic often does not need a separate preposition here. Heim itself already expresses movement toward home.

Because the subject is still the same: hún.

In coordinated clauses, Icelandic often leaves out a repeated subject if it is clear from context:

• fór hún út að ganga ... og kom síðan rólegri heim

This means:

• she went out for a walk ... and then came home calmer

Repeating hún would also be possible in some contexts, but omitting it is very normal and natural.

Síðan here means then, afterward, or after that.

It links the two actions in sequence:

1. she went out for a walk
2. síðan she came home calmer

So it helps show the timeline of events.

Yes.

• fara = to go

• fór = went

• koma = to come
• kom = came

These are common verbs, and both have irregular past forms, so they need to be learned as vocabulary rather than built with a simple ending.

It breaks down like this:

• Eftir rifrildið = After the argument
• fór hún út að ganga í smástund = she went out for a walk for a short while
• og kom síðan rólegri heim = and then came home calmer

So the sentence describes:

1. a starting point in time
2. an action
3. a later result or changed state

That final part, kom síðan rólegri heim, is especially useful to notice: Icelandic often uses come/go/become + adjective to describe how someone ends up after an event.