Hún svarar stutt og fer svo heim.

Because hún is the subject of the sentence: she is the one doing the actions.

In this sentence, hún does two things:

• svarar = answers
• fer = goes

So Icelandic uses the nominative subject form hún.

svarar is the present tense of the verb að svara = to answer.

So:

• að svara = to answer
• hún svarar = she answers / she is answering

In Icelandic, the present tense often covers both simple present and present progressive meanings, depending on context.

Here stutt is being used adverbially, meaning briefly / shortly.

The basic adjective is:

• stuttur = short

But Icelandic often uses the neuter singular form of an adjective as an adverb. So:

• stuttur = short (masculine adjective)
• stutt = short / briefly (used adverbially here)

So Hún svarar stutt means she answers briefly, not that something is grammatically feminine or masculine.

Yes. Stuttlega also means briefly.

The difference is mostly style and feel:

• stutt = very common, natural, compact
• stuttlega = also correct, sometimes a bit more formal or explicit

So both are possible, but svara stutt is a very natural everyday expression.

Because að fara = to go is an irregular verb.

Its present tense is:

• ég fer = I go
• þú ferð = you go
• hann/hún/það fer = he/she/it goes

So fer is simply the correct 3rd person singular present form.

Here svo means then / after that.

So the sequence is:

1. she answers briefly
2. then she goes home

In other contexts, svo can also mean things like so, thus, or be part of other expressions, but in this sentence then is the most natural interpretation.

Because Icelandic, like English, often does not repeat the subject when two verbs share the same subject and are linked by og = and.

So:

• Hún svarar stutt og fer svo heim.

means:

• She answers briefly and then goes home.

You could repeat hún, but it would usually sound less natural unless you wanted extra emphasis:

• Hún svarar stutt og hún fer svo heim.

That is grammatical, just less neutral here.

In this sentence, heim is a directional adverb meaning homeward / home.

So:

• fara heim = go home

This is similar to English, where we also say go home without to.

Compare:

• heim = home, toward home
• heima = at home

So:

• Hún fer heim. = She goes home.
• Hún er heima. = She is at home.

That is a very important and common Icelandic distinction.

Because Icelandic uses heim by itself after verbs of motion.

So English:

• go home

matches Icelandic:

• fara heim

You do not say a separate word corresponding to to here.

This is normal and very common in Icelandic with certain place adverbs such as heim.

The word order is very normal.

The basic structure is:

• Hún svarar stutt = She answers briefly
• og fer svo heim = and then goes home

A few things to notice:

• the finite verb comes early, as usual in Icelandic
• svo comes after fer here
• the second clause keeps the same subject without repeating hún

You may also see other word orders in Icelandic depending on emphasis, but this sentence is straightforward and idiomatic.

Not always. It can appear without an expressed object, as it does here.

So Hún svarar stutt means:

• She answers briefly.

If you want to say she answers him/her, Icelandic usually uses the dative:

• Hún svarar honum. = She answers him.
• Hún svarar henni. = She answers her.

So this sentence simply leaves out the person being answered because it is not important or is already understood from context.

A rough English-friendly approximation is:

• Hoon svar-ar stut and fer svo haym

A few notes:

• ú in hún is a long oo sound
• sv in svarar is pronounced together, close to sv
• tt in stutt is pronounced with Icelandic consonant quality, not exactly like English
• ei in heim sounds like ay in day, but not exactly

A more Icelandic-style rough guide would be:

• Hoon svar-ar stut og fer svo haym

But pronunciation varies a bit by speaker and accent, so this is only an approximation.