Ég svara þér þegar ég kem heim.

Because svara takes the dative case in Icelandic.

• þér = you (dative singular)
• þig = you (accusative singular)

So after svara, Icelandic uses the dative:

• Ég svara þér = I answer you / I reply to you

This is something learners usually just have to memorize with the verb: svara + dative.

In Icelandic, the present tense is very often used for future meaning, especially when the future event is understood from context.

So Ég svara þér þegar ég kem heim literally uses present forms, but it naturally means something like I’ll answer you when I get home.

This is very normal Icelandic. English often prefers will, but Icelandic often does not need an equivalent future marker.

Yes. Mun is used to make the future more explicit:

• Ég svara þér þegar ég kem heim = natural, everyday way
• Ég mun svara þér þegar ég kem heim = I will answer you when I get home

The version without mun is usually more common in ordinary speech. Using mun can sound a bit more explicit, formal, or emphatic.

Because kem is the 1st person singular present tense form of koma (to come).

The verb changes like this:

• að koma = to come
• ég kem = I come
• þú kemur = you come
• hann/hún/það kemur = he/she/it comes

So in þegar ég kem heim, the subject is ég, so the correct form is kem.

It is at least partly irregular from a learner’s point of view, because the stem vowel changes:

• infinitive: koma
• present singular: kem, kemur
• past: kom
• past participle: komið

That o → e change in the present singular is not something you can predict purely from the infinitive unless you already know the pattern, so it is worth memorizing.

This is a very common distinction in Icelandic:

• heim = home, homewards (movement toward home)
• heima = at home (location, no movement)

So:

• ég kem heim = I come home / I get home
• ég er heima = I am at home

In your sentence, the speaker is moving to home, so heim is correct.

English can say answer you or reply to you, depending on the verb. Icelandic uses the verb svara, and that verb directly takes a dative object.

So Icelandic does not need a separate word corresponding to English to here:

• Ég svara þér

The relationship is shown by the case of þér, not by a preposition.

Þegar usually means when.

In a sentence like this, it introduces a time clause:

• þegar ég kem heim = when I get home

Depending on context, English might translate it as when, once, or even as soon as, but the basic meaning is simply when.

Because after the conjunction þegar, Icelandic normally uses subordinate clause word order.

That means the subject usually comes before the verb:

• þegar ég kem heim

This is different from main-clause word order, where Icelandic often follows the verb-second pattern. In subordinate clauses introduced by words like þegar, að, ef, sem, and so on, the subject commonly appears before the finite verb.

Not really in this sentence. Here heim functions more like an adverb of direction than an ordinary noun.

That is why there is no article and no visible case ending like you might expect with a normal noun phrase. It behaves more like English home in go home than like a regular noun such as house.

The letter þ is pronounced like the th in thin, not like the th in this.

So:

• þér starts with the voiceless th sound
• þegar also starts with that same sound

English speakers often confuse þ and ð:

• þ = like th in thin
• ð = usually like th in this (though pronunciation can vary by position)

In normal Icelandic, the subject pronoun is usually stated clearly, so ég appears in both clauses:

• Ég svara þér
• þegar ég kem heim

Unlike some languages, Icelandic does not normally drop subject pronouns just because the verb form already shows the person. So repeating ég is natural and expected.

It is neutral and natural. It works well in everyday speech and writing.

A few notes:

• þér here is not especially formal; it is simply the correct dative form of singular you
• the sentence sounds straightforward and idiomatic
• if you wanted a more explicitly future-sounding version, you could use mun, but that is not necessary

So this is a very normal way to say it in Icelandic.