Hún grætur stundum í barnavagninum, en móðirin nær alltaf að hugga hana.

It can potentially cover both, because Icelandic does not have a separate everyday verb form exactly like the English is crying.

In this sentence, because of stundum (sometimes), the meaning is clearly habitual, so cries is the best English match.

The base verb is gráta = to cry.

Gráta is the dictionary form, meaning to cry.
Grætur is the 3rd person singular present form, used with hún (she).

So:

• að gráta = to cry
• hún grætur = she cries

This is just normal verb conjugation.

Stundum means sometimes.

Its position is normal. In a simple Icelandic main clause, the finite verb usually comes early, and adverbs like stundum often come after it:

• Hún grætur stundum = She sometimes cries

You may see adverbs move around a bit in Icelandic, but this placement is very common and natural.

Because í can take different cases depending on meaning:

• location = usually dative
• movement into something = usually accusative

Here the meaning is in the stroller / in the pram, so it is location, and that is why Icelandic uses the dative.

The noun is:

• barnavagn = stroller / pram / baby carriage

And barnavagninum means the stroller in the dative singular definite.

So:

• í barnavagninum = in the stroller

The ending -num is a very common masculine/neuter dative singular definite ending.

Because móðirin means the mother, while móðir means just mother.

Icelandic usually puts the definite article at the end of the noun as a suffix:

• móðir = mother
• móðirin = the mother

In this sentence, it refers to a specific mother already understood from the context, so móðirin is natural.

En usually means but in a sentence like this.

It connects two clauses and shows a contrast:

• she sometimes cries
• but the mother manages to comfort her

In some contexts en can feel closer to and, but here but is the best fit.

No. In this sentence, nær is the verb ná in the present tense.

Here ná að + infinitive means to manage to or to succeed in doing something.

So:

• móðirin nær ... að hugga hana = the mother manages ... to comfort her

This is important, because an English speaker might mistake nær alltaf for nearly always. But that is not what is happening here.

Here the structure is:

• nær = manages
• alltaf = always

So the sense is always manages to comfort her.

If you wanted nearly always, Icelandic would more naturally use næstum alltaf.

Because the verb ná in this meaning is followed by að + infinitive.

So the pattern is:

• ná að gera eitthvað = manage to do something

Here:

• ná að hugga hana = manage to comfort her

The word að is the infinitive marker, similar to English to in to comfort.

Yes. These are different case forms of the same pronoun:

• hún = she (nominative, used for the subject)
• hana = her (accusative, used for a direct object)
• henni = her (dative)

The verb hugga takes a direct object in the accusative, so Icelandic uses hana:

• að hugga hana = to comfort her

That is why the sentence has:

• Hún grætur ... = She cries ...
• móðirin nær að hugga hana = the mother manages to comfort her

Yes. It is very typical.

The sentence has two main clauses joined by en:

• Hún grætur stundum í barnavagninum
• en móðirin nær alltaf að hugga hana

In Icelandic main clauses, the finite verb normally appears in the second position. This is often called V2 word order.

So in the first clause:

• Hún = first element
• grætur = finite verb in second position

And in the second clause:

• móðirin = first element
• nær = finite verb in second position

That is one reason Icelandic word order can feel a bit different from English, but this sentence is very standard.