Þau rífast stundum um það hver eigi að elda, en þau hlusta samt á hvort annað á endanum.

Þau is the neuter plural form of they. In Icelandic, that is often used for:

• a mixed-gender group,
• a group whose gender is unknown or unimportant,
• children.

So here þau is a normal way to say they if the group is mixed or not specifically identified as all male or all female.

Rífast means to argue / quarrel / bicker.

The -st ending is very common in Icelandic and often marks a middle-voice or reflexive-type verb. These verbs do not always translate neatly into English reflexives, but they often have meanings like:

• acting mutually,
• acting on oneself,
• being in a certain state.

In this sentence, þau rífast means they argue or they argue with each other.

So you do not need to add a separate word for each other after rífast. The verb already works that way naturally.

Here um það introduces the content of the argument: about who should cook.

Literally, it is something like:

• um = about
• það = that

But in natural English we usually do not translate the það directly. Icelandic often uses this kind of anticipatory það before a clause.

So:

• um það hver eigi að elda

is naturally understood as:

• about who should cook
• or more literally, about the question of who should cook

The það makes the structure sound natural in Icelandic, even though English usually leaves it out.

Because this is an embedded question rather than a direct question.

Compare:

• Direct question: Hver á að elda? = Who should cook?
• Embedded question: ... um það hver eigi að elda = ... about who should cook

Here eigi is the present subjunctive of eiga. In Icelandic, the subjunctive is often used in clauses like this when the matter is unsettled, uncertain, or being discussed rather than simply stated as a fact.

Also, hver is grammatically singular, so the verb is singular too. That is why you get eigi, not a plural form.

In this sentence, eiga að elda means should cook, is supposed to cook, or ought to cook.

So although eiga often means to own / have, in the pattern eiga að + infinitive it has a different meaning:

• ég á að fara = I should go / I am supposed to go
• hver eigi að elda = who should cook

This is a very common Icelandic structure.

They look similar, but they are doing very different jobs.

• hver here means who
• hvort annað means each other / one another

So:

• hver eigi að elda = who should cook
• hlusta á hvort annað = listen to each other

In hvort annað, hvort is part of a reciprocal expression, not the same thing as the hver meaning who.

Also, the form hvort annað matches the neuter subject þau, which is why this form is used here.

In Icelandic, hlusta normally takes á when you say who or what someone is listening to.

So:

• hlusta á einhvern = listen to someone
• hlusta á tónlist = listen to music
• hlusta á hvort annað = listen to each other

This is just the standard pattern of the verb. English says listen to, while Icelandic says hlusta á.

Hvort annað is a reciprocal expression meaning each other.

In this sentence, it is used after the preposition á, so the whole phrase means:

• á hvort annað = to each other

Why this form?

• the subject is þau, which is neuter plural in form,
• so the reciprocal expression also appears in a neuter form,
• and after á here, the form used is hvort annað.

For a learner, the easiest way to remember it is simply:

• hlusta á hvort annað = listen to each other

It is a very useful chunk to learn as a set phrase.

Not really. They work together very naturally.

• en = but
• samt = still / nevertheless / all the same

So:

• en þau hlusta samt ...

means something like:

• but they still listen ...
• but they nevertheless listen ...

English often does the same thing:

• They argue, but they still listen to each other.

So samt adds emphasis to the contrast.

Á endanum means in the end / eventually / at the end.

Literally:

• á = at / on
• endanum = the end in the dative singular definite form

So the phrase is literally something like at the end.

In this sentence, it functions as an adverbial expression meaning:

• in the end
• in the final outcome

It is best learned as a whole expression:

• á endanum = in the end

This is mainly because of normal Icelandic word order, especially the verb-second pattern in main clauses.

In both main clauses, the subject comes first, and the finite verb comes right after it:

• Þau rífast stundum ...
• en þau hlusta samt ...

Then adverbs like stundum and samt often come after the verb.

So the order is very natural:

• Þau rífast stundum = They argue sometimes
• þau hlusta samt = they still listen

You could move some adverbs for emphasis, but the version in the sentence is neutral and natural Icelandic.