Þau horfðu á hvort annað og hlógu þegar tappinn datt af flöskunni.

Yes. Þau is the 3rd person plural pronoun, and it is commonly used for:

• a mixed-gender group
• a group whose gender is unknown or not important
• sometimes a more neutral they

So in this sentence, Þau horfðu... simply means They looked...

If the group were specifically all male, you would usually see Þeir.
If it were specifically all female, you would usually see Þær.

The verb is horfa á, which means to look at / watch.

So:

• horfðu = looked
• á = part of the verb expression

In Icelandic, many verbs naturally go with a preposition, and you have to learn them together.
Here, horfa usually needs á when you say what someone is looking at.

Examples:

• horfa á sjónvarpið = watch the television
• horfa á mig = look at me

So horfðu á hvort annað literally means looked at each other.

Hvort annað means each other / one another.

It is the standard Icelandic reciprocal expression used when two or more people do something to one another.

In this sentence:

• Þau horfðu á hvort annað = They looked at each other

A useful thing to know is that hvort annað changes form depending on grammar, especially case and sometimes gender/number context. In this sentence, it is the form needed after á with horfa á.

Because the expression has to fit the grammar of the verb phrase horfa á.

Here, á in horfa á takes the object in the accusative, so the reciprocal expression appears in its accusative form: hvort annað.

Learners often first meet hvort annað as a fixed phrase meaning each other, but it is not completely fixed. It can change depending on case.

So the important point here is:

• horfa á + accusative
• therefore hvort annað is in the accusative form here

Because hlæja (to laugh) is an irregular verb.

Its past tense is not built in a simple regular way. The past plural form is:

• hlógu = laughed

So:

• ég hlæ = I laugh
• þau hlógu = they laughed

This is something you mostly need to memorize. Icelandic has quite a few common strong or irregular verbs whose past tense changes the vowel.

Þegar means when.

It introduces a subordinate clause:

• þegar tappinn datt af flöskunni = when the cork fell off the bottle

So the whole sentence has two linked parts:

1. Þau horfðu á hvort annað og hlógu
2. þegar tappinn datt af flöskunni

In other words: they looked at each other and laughed when the cork came/fell off the bottle.

Because -inn is the definite article attached to the noun.

• tappi = a cork / a stopper
• tappinn = the cork / the stopper

Here, tappinn is the subject of datt, so it is in the nominative singular definite form.

Icelandic usually adds the definite article to the end of the noun rather than using a separate word like English the.

Datt is the past tense of detta, which means to fall.

So:

• detta = to fall
• datt = fell

This is another irregular verb. The sentence literally says:

• tappinn datt af flöskunni = the cork fell off the bottle

In natural English, this might also be translated as the cork popped off the bottle, depending on context.

Because the preposition af normally takes the dative case when it means off / from.

The noun is flaska = bottle.
Its definite singular dative form is flöskunni = the bottle.

So:

• flaska = bottle
• flöskan = the bottle
• af flöskunni = off the bottle / from the bottle

This is a very typical Icelandic pattern:

• preposition
• required case
• noun changes form accordingly

That is due to Icelandic noun inflection and vowel change.

The noun flaska declines like this in the singular:

• flaska = nominative
• flösku = accusative / dative base form
• flösku / flösku- appears in oblique cases
• flöskunni = dative definite

So the vowel changes from a to ö in the oblique stem. This kind of stem change is common in Icelandic and is something learners gradually get used to.

Good question. Icelandic is a verb-second language in main clauses, but subordinate clauses behave differently.

After a subordinating conjunction like þegar, the clause usually has more normal subordinate-clause order:

• þegar tappinn datt af flöskunni

So here you get:

• þegar
  • subject + verb + rest

That is completely normal.

Compare the main clause:

• Þau horfðu á hvort annað og hlógu

with the subordinate clause:

• þegar tappinn datt af flöskunni

Yes. Af often covers both off and from, depending on context.

In this sentence, since the subject is the cork, English naturally prefers:

• fell off the bottle
• came off the bottle
• popped off the bottle

But grammatically, af is the normal Icelandic preposition here for separation from the surface or attachment point.

The sentence most naturally means that they looked at each other and laughed when the cork fell off the bottle.

So the when-clause gives the time of the laughing and looking. In context, it often also suggests that the falling cork was the reason or trigger, but grammatically þegar mainly marks time, not explicit cause.

If you wanted to state cause more directly, Icelandic might use something like af því að for because.

Yes. Icelandic often uses a verb meaning fall in places where English might choose a more specific verb.

So tappinn datt af flöskunni is perfectly natural Icelandic. Depending on the situation, idiomatic English could be:

• the cork fell off the bottle
• the cork came off the bottle
• the cork popped off the bottle

The Icelandic wording is straightforward and natural.