Ég skal láta þig vita þegar ég kem heim.

Skal is the 1st person singular form of skulu. In this sentence, ég skal means something like:

• I will
• I’ll make sure to
• I promise I will

It is not as old-fashioned as English shall can sound. In modern Icelandic, ég skal is completely normal.

In this sentence, ég skal láta þig vita has a slightly reassuring or promise-like tone: I’ll let you know.

This is a very common Icelandic expression.

• láta = let, make, cause
• vita = know

Together, láta einhvern vita means to let someone know or to inform someone.

So:

• láta þig vita = let you know
• láta mig vita = let me know
• láta okkur vita = let us know

You should learn this as a set phrase, because it is extremely common in everyday Icelandic.

Because þig is the object form of þú.

• þú = you (subject form)
• þig = you (object form)

In Ég skal láta þig vita, the person being informed is the object of the verb phrase, so Icelandic uses þig.

Compare:

• Þú kemur heim. = You come home.
  Here þú is the subject.

• Ég sé þig. = I see you.
  Here þig is the object.

The same thing is happening in láta þig vita.

Because kem is the correct conjugated form for ég.

The verb is koma = to come, but Icelandic verbs change form depending on the subject.

Present tense of koma:

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

So þegar ég kem heim means when I come home.

This is just an irregular verb, so kem has to be memorized.

Because Icelandic often uses the present tense in time clauses referring to the future, especially after words like þegar = when.

So Icelandic says:

• þegar ég kem heim
  literally: when I come home

Even though the meaning is future, the present tense is natural here.

English does something very similar:

• I’ll call you when I get home.

You do not normally say when I will get home in standard English, and Icelandic works similarly here.

In this sentence, þegar means when.

So:

• þegar ég kem heim = when I get home / when I come home

Be aware that þegar can also mean already in other contexts, which can confuse learners.

For example:

• Ég er þegar kominn heim. = I am already home.

So the word þegar has more than one use, but in your sentence it is clearly the conjunction when.

Because heim is a special adverb meaning homeward / home / to home.

In Icelandic, you often do not need a preposition here.

• fara heim = go home
• koma heim = come home
• keyra heim = drive home

This is similar to English, where we also usually say go home, not go to home.

A very useful contrast is:

• heim = motion toward home
• heima = at home

So:

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

Yes, absolutely. That would also be natural.

• Ég læt þig vita þegar ég kem heim.
• Ég skal láta þig vita þegar ég kem heim.

Both can mean I’ll let you know when I get home, but there is a small difference in tone:

• Ég læt þig vita ... = more neutral, often just a statement of intention
• Ég skal láta þig vita ... = slightly stronger, more like a promise or assurance

So skal adds emphasis: I will definitely let you know.

Both can refer to the future, but they are not always interchangeable.

Very roughly:

• ég mun ... = neutral future, prediction, statement about what will happen
• ég skal ... = willingness, decision, promise, assurance, sometimes obligation depending on context

In this sentence, ég skal láta þig vita sounds very natural because the speaker is promising to do something.

Compare:

• Ég mun hringja á morgun. = I will call tomorrow.
  Neutral future.

• Ég skal hringja á morgun. = I’ll call tomorrow.
  More like I promise / I’ll make sure to.

So skal is a good choice here.

Because þegar introduces a subordinate clause, and Icelandic word order changes in subordinate clauses.

In a subordinate clause, the normal order is:

• conjunction + subject + finite verb

So:

• þegar ég kem heim = when I come home

Not:

• þegar kem ég heim

That second order would sound wrong here.

This is a useful contrast:

• Kem ég heim? = Am I coming home? / Will I come home?
  Verb-first, as in a question

• þegar ég kem heim = when I come home
  Subject before verb in the subordinate clause

Yes. Icelandic allows different word order patterns, as long as the grammar rules are followed.

For example, you can also say:

• Þegar ég kem heim, skal ég láta þig vita.

That means the same thing.

Notice what happens in the main clause after the initial subordinate clause:

• skal ég láta þig vita

This is because Icelandic main clauses usually follow the verb-second pattern. When the sentence starts with Þegar ég kem heim, that whole clause takes the first position, so the finite verb skal comes next.

So both of these are correct:

• Ég skal láta þig vita þegar ég kem heim.
• Þegar ég kem heim, skal ég láta þig vita.

The first one is probably the more straightforward version for a learner.

Yes, people really would say this. It sounds natural and everyday.

It is neither especially formal nor unusually literary. The phrase láta þig vita is very common in speech, messages, and normal conversation.

If anything, the version with skal may sound a little more deliberate or reassuring than a plain present tense version, but it is still completely normal.