Hún talar hljóðlátt þegar barnið sefur.

Here hljóðlátt is functioning as an adverb, not as an adjective modifying a noun.

In Icelandic, many adverbs are formed from the neuter singular form of an adjective. The adjective hljóðlátur means quiet:

• masculine: hljóðlátur
• feminine: hljóðlát
• neuter: hljóðlátt

When used adverbially, the neuter form often means quietly. So:

• hún er hljóðlát = she is quiet
• hún talar hljóðlátt = she speaks quietly

So the -tt ending is not agreeing with hún; it is showing the adverbial form.

Talar is the present-tense form of tala, which can mean both talk and speak, depending on context.

So hún talar hljóðlátt could be understood as:

• she speaks quietly
• she talks quietly

English often distinguishes speak and talk more sharply than Icelandic does, so tala covers both in many situations.

Because barnið is the definite form: the child.

• barn = a child / child
• barnið = the child

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

So the ending -ið here is the suffixed definite article.

Because Icelandic grammatical gender is not always the same as natural gender.

The noun barn is grammatically neuter, so:

• barn
• barnið

This does not mean the child is biologically or socially neuter. It only means the noun belongs to the neuter grammatical class.

That is very common in Icelandic and other gendered languages. A noun’s grammatical gender is something you usually just have to learn with the word.

Because sofa is an irregular verb.

Its infinitive is sofa = to sleep, but in the present tense, the stem changes:

• ég sef = I sleep
• þú sefur = you sleep
• hann / hún / það sefur = he / she / it sleeps

So barnið sefur simply means the child sleeps / is sleeping.

This vowel change from o to e is something learners have to memorize for this verb.

Here þegar introduces a time clause and usually means when. In natural English, this sentence may also feel close to while, depending on context.

So þegar barnið sefur means:

• when the child sleeps
• sometimes naturally understood as when/while the child is asleep

The exact English wording depends on context, but grammatically þegar is the conjunction introducing the subordinate time clause.

Both are in the nominative, because each is the subject of its clause.

• Hún is the subject of talar
• barnið is the subject of sefur

So the sentence has:

• main clause: Hún talar hljóðlátt
• subordinate clause: þegar barnið sefur

Each clause has its own subject.

Yes, absolutely.

That version is also correct:

• Hún talar hljóðlátt þegar barnið sefur.
• Þegar barnið sefur, talar hún hljóðlátt.

A very important point is that Icelandic normally puts the finite verb in second position in the main clause. So if the subordinate clause comes first, the verb talar comes before the subject hún:

• Þegar barnið sefur, talar hún hljóðlátt.

You would not normally say Þegar barnið sefur, hún talar hljóðlátt.

Because a comma is not required here.

In Icelandic, punctuation does not always match English punctuation. A short subordinate clause introduced by þegar is often written without a comma in a sentence like this:

• Hún talar hljóðlátt þegar barnið sefur.

If the þegar-clause comes first, a comma is more naturally used after it:

• Þegar barnið sefur, talar hún hljóðlátt.

So the lack of a comma in your sentence is normal.

It can be either, depending on context.

Hún talar hljóðlátt þegar barnið sefur can mean:

• a habitual action: she speaks quietly whenever the child is asleep
• a current situation: she is speaking quietly because the child is asleep

Icelandic present tense often covers both meanings, just like English sometimes does. Context tells you which interpretation is intended.