Hún snýr sér hægt við og brosir.

Because snúa sér við is the usual reflexive expression for turn around or turn oneself around.

The word sér is the reflexive pronoun, meaning something like herself here. Icelandic often uses a reflexive pronoun in places where English does not.

So:

• snúa sér við = turn around
• literally, something close to turn oneself around

Without sér, the meaning would usually change or sound incomplete in this context.

Sér is the reflexive pronoun, used for himself / herself / itself / themselves depending on context.

In this sentence, since hún means she, sér means herself.

A useful point: sér does not change for gender. The subject tells you who it refers to.

Examples:

• Hún sér sig. = She sees herself.
• Hún snýr sér við. = She turns around.

In your sentence, sér is in the case required by the verb expression snúa sér við.

Because the verb phrase snúa sér við takes the reflexive pronoun in the dative, not the accusative.

Very roughly:

• sig = accusative reflexive
• sér = dative reflexive
• sín = genitive reflexive

This is something you often just have to learn with the verb or expression.

So the pattern is:

• snúa sér við = turn around

not

• snúa sig við

No. Here við is not the preposition with.

In this sentence, við is part of the verb expression snúa sér við, which means turn around.

So it functions more like a verbal particle. English has similar things in phrasal verbs:

• turn around
• sit down
• wake up

Here, við helps create the meaning around/back rather than with.

Hægt is the neuter singular form of the adjective hægur (slow), and Icelandic often uses that form adverbially.

So:

• hægur = slow (adjective)
• hægt = slowly (adverbial use)

This is very common in Icelandic. English usually has a separate -ly adverb, but Icelandic often uses the neuter adjective form instead.

So:

• Hún gengur hægt. = She walks slowly.
• Hún snýr sér hægt við. = She turns around slowly.

Here hægt comes before við, inside the verb phrase:

• snýr sér hægt við

That placement sounds natural and idiomatic.

Icelandic adverb placement can be somewhat flexible, but not all positions sound equally natural. In this sentence, hægt fits well between sér and við because við belongs closely with snýr sér as part of the expression snúa sér við.

So learners should probably treat snúa sér við as a unit, while remembering that an adverb can appear inside it:

• snýr sér hægt við

Brosir is the simple present tense of brosa (to smile).

Icelandic often uses the simple present where English might use either:

• smiles
• is smiling

So brosir can cover both kinds of meaning depending on context.

The form vera að + infinitive (like er að brosa) does exist and can emphasize an ongoing action, similar to English progressive is smiling, but it is not required here.

So this sentence is perfectly natural with just:

• brosir

Because both verbs share the same subject.

In English, we also often do this:

• She turns around slowly and smiles.

Icelandic works the same way here:

• Hún snýr sér hægt við og brosir.

The subject hún applies to both snýr and brosir, so there is no need to repeat it.

You could repeat it in some contexts for emphasis, but normally you would not.

Both are present tense, third person singular.

Because the subject is hún (she), the verbs are in the he/she/it form.

• snýr = turns / is turning
• brosir = smiles / is smiling

So the sentence describes what she does in the present, or in a narrative present style.

That is just the present-tense form of the verb.

The dictionary form is:

• snúa = to turn

But in the present tense, third person singular, it becomes:

• hann/hún/það snýr = he/she/it turns

This kind of vowel change is normal in Icelandic verbs and is something learners gradually get used to.

So you should learn the pair:

• snúa → snýr

just as:

• brosa → brosir

It can suggest either very close sequence or overlapping actions, depending on context.

• First she turns around, then she smiles.
• Or she turns around slowly and smiles as she does it.

The conjunction og simply means and, so it links the two actions without forcing a very strict interpretation.

In most contexts, a listener would understand it naturally from the situation.

Yes, definitely.

It is very helpful to learn this as a chunk:

• snúa sér við = turn around

That is better than trying to build it from separate words every time, because:

• the reflexive pronoun is required
• the pronoun is in the dative
• við is part of the expression

So for a learner, this is a great example of a phrase worth memorizing whole.