Hann kyssir eiginkonu sína á kinnina áður en hann fer í vinnu.

Kyssa is the infinitive, meaning to kiss. In the sentence you need a finite verb, because the subject is hann. The form kyssir is the present tense, 3rd person singular:

• að kyssa = to kiss
• hann kyssir = he kisses

So Hann kyssir ... means He kisses ...

Because eiginkonu is the accusative singular form, and kyssa takes a direct object in the accusative.

• eiginkona = wife, in the dictionary form, usually nominative
• eiginkonu = wife, as a direct object

So:

• eiginkona = wife
• hann kyssir eiginkonu ... = he kisses a wife / his wife

This is a very common thing in Icelandic: nouns change form depending on their grammatical role.

Because sína is the reflexive possessive pronoun. It refers back to the subject of the clause, which here is hann.

So:

• eiginkonu sína = his own wife
• eiginkonu hans = his wife, but not necessarily the subject’s own wife; it can sound like the wife of some other man

In other words, Icelandic makes a clear distinction that English usually does not. Since the man is kissing his own wife, sína is the natural choice.

The pronoun comes from sinn, and it has to agree with the thing possessed, not with the possessor.

Here the possessed noun is eiginkonu, which is:

• feminine
• singular
• accusative

So the matching form is sína.

That is why you get:

• eiginkonu sína

not some other form of sinn.

This means on the cheek. With verbs like kyssa, Icelandic commonly uses á plus the body part:

• kyssa einhvern á kinnina = kiss someone on the cheek

So the structure is very normal and idiomatic.

English speakers sometimes expect something more like kiss on the cheek as a fixed chunk, but in Icelandic it is built with:

• kyssa
  • person in the accusative
• á
  • body part

Because kinnina means the cheek. Icelandic usually attaches the definite article to the end of the noun.

So:

• kinn = cheek
• kinnina = the cheek, in the accusative singular

The sentence is talking about a specific cheek, so the definite form is used.

The preposition á can take either accusative or dative, depending on meaning and construction. In this expression, á kinnina is the normal idiomatic form.

A useful way to think about it is that the action is directed toward the cheek, so accusative is used. This kind of accusative is common with expressions involving physical contact aimed at a body part.

So learners should mostly remember the whole pattern:

• kyssa einhvern á kinnina

rather than trying to translate word-for-word from English.

Because áður en hann fer í vinnu is a full subordinate clause, and that clause needs its own subject.

Even though it is the same person as in the main clause, Icelandic normally still states the subject:

• Hann kyssir ... áður en hann fer í vinnu

English does the same here:

• He kisses ... before he goes to work

So the second hann is completely normal.

Because áður en introduces a subordinate clause, and subordinate clauses do not follow the normal main-clause verb-second pattern in the same way.

So after áður en, the regular order is:

• áður en hann fer ...

not:

• áður en fer hann ...

This is an important Icelandic pattern:

• main clauses often show verb-second word order
• subordinate clauses usually keep subject + verb order

Because fara í vinnu is a standard Icelandic expression meaning go to work or go off to work.

So:

• fara í vinnu = go to work
• vera í vinnu = be at work / be working

English uses to work, but Icelandic uses í here. This is something best learned as a set phrase.

Yes. You can say:

Áður en hann fer í vinnu kyssir hann eiginkonu sína á kinnina.

That is perfectly good Icelandic. Notice what happens in the main clause after the fronted subordinate clause:

• Áður en hann fer í vinnu = first element
• then the finite verb comes next: kyssir
• then the subject: hann

So this version nicely shows Icelandic verb-second word order in the main clause.