Lyklasmiðurinn kemur í dag til að laga lásinn.

Because Icelandic very often makes compound nouns and writes them as a single word.

Lyklasmiðurinn can be broken down like this:

• lykla- = a compound form related to lykill (key)
• smiður = smith / craftsman
• -inn = the

So lyklasmiðurinn means the locksmith.
A native English speaker may want to separate it into something like key smith, but Icelandic normally keeps this as one word.

In Icelandic, the definite article is usually attached to the noun instead of being a separate word.

So:

• lyklasmiður = locksmith
• lyklasmiðurinn = the locksmith

And similarly:

• lás = lock
• lásinn = the lock

This is one of the first big differences from English. Icelandic does have a separate form related to the in some contexts, but in ordinary sentences like this, the attached ending is the normal choice.

Yes. Lyklasmiður is the normal word for locksmith.

The literal parts of Icelandic compounds do not always match the most natural English word-for-word translation. So even if the word looks like key-smith, the correct English equivalent here is still locksmith.

Because Icelandic often uses the present tense for a future event, especially when it is planned, expected, or scheduled.

So:

• Lyklasmiðurinn kemur í dag
  can mean The locksmith is coming today

This works much like English in sentences such as He comes tomorrow or The train leaves at six, although English often prefers is coming in everyday speech.

Here kemur is the 3rd person singular present of koma (to come).

Í dag is a fixed Icelandic time expression meaning today.

Literally, í often means in, but in expressions like this you should learn the whole phrase together:

• í dag = today
• í morgun = this morning
• í kvöld = tonight / this evening

So it is best not to translate í too mechanically here. The whole phrase simply functions as a time expression.

Til að means to or in order to when expressing purpose.

So:

• kemur í dag til að laga lásinn
  = is coming today to fix the lock

It answers the question why is he coming?
Answer: to fix the lock.

Because after til að, Icelandic uses the infinitive form of the verb.

So:

• að laga = to fix
• lagar = fixes

In this sentence, the main conjugated verb is kemur (comes / is coming).
The phrase til að laga lásinn is not a separate full clause with its own finite verb. It is a purpose phrase: to fix the lock.

Good question. The að you see here is already doing the job needed before the infinitive.

Dictionary forms are usually written with að:

• að koma
• að laga

But inside a sentence, you do not automatically keep adding extra aðs.
So you say:

• til að laga

not:

• til að að laga

Think of til að as the normal structure meaning in order to, followed by the infinitive.

Because lásinn is the direct object of laga.

The thing being fixed is the lock, so Icelandic uses the object form required by the verb. In this case:

• lás = lock
• lásinn = the lock

For this noun, the relevant singular forms happen to look the same in nominative and accusative when definite, so you do not see a visible change beyond the article ending. But syntactically, it is the object of laga.

Yes. Icelandic word order is flexible, but main clauses usually follow the verb-second pattern.

The sentence as given is:

• Lyklasmiðurinn kemur í dag til að laga lásinn.

You can also say:

• Í dag kemur lyklasmiðurinn til að laga lásinn.

That version puts emphasis on today. Notice that the verb kemur still stays in the second position.

What you normally do not say is:

• Í dag lyklasmiðurinn kemur ...

because that breaks the usual verb-second pattern.

They are part of the spelling and represent different vowels, not just optional stress marks.

For example:

• i and í are different vowels
• a and á are different vowels

So í is not just i with emphasis, and lás is not just las with stress. The accents matter and can change pronunciation and meaning.

Also, Icelandic normally stresses the first syllable of a word, so these accents are not mainly there to show stress the way an English speaker might assume.