Áður en helgin byrjar vil ég láta klippa hárið, láta laga lásinn og láta stytta faldinn.

Áður en is the normal way to say before when it introduces a whole clause with its own verb, like helgin byrjar.

• áður en helgin byrjar = before the weekend starts

If you only have a noun phrase, Icelandic often uses fyrir instead:

• fyrir helgi = before the weekend

So áður en is a fixed conjunction pattern here.

Helgin is the definite form, meaning the weekend. In this sentence, the speaker means a specific weekend, most likely the upcoming one, so the definite form is natural.

Also, helgin is the subject of byrjar:

• helgin byrjar = the weekend starts

Icelandic very often uses the present tense for future time when the event is expected, planned, or obvious from context.

So helgin byrjar can mean the weekend starts / is going to start. This is similar to English sentences like My flight leaves tomorrow.

This is because Icelandic follows a verb-second pattern in main clauses. When a different element comes first, the finite verb usually comes next.

Here the sentence begins with the subordinate clause Áður en helgin byrjar, so that fills the first slot. Then the finite verb of the main clause comes next:

• Áður en helgin byrjar vil ég ...

If the sentence began directly with the subject, then you would get:

• Ég vil ...

Here láta means something like have something done or arrange for something to be done. It is a very common Icelandic way to talk about services.

So:

• láta klippa hárið = have one’s hair cut
• láta laga lásinn = have the lock repaired
• láta stytta faldinn = have the hem shortened

The person who does the action is not mentioned, because it is not important here.

Some Icelandic verbs take a bare infinitive, without að. Both vilja and láta do that.

So you get:

• vil ég láta klippa ...
• not vil ég láta að klippa ...

This is something learners just have to get used to: some verbs require að, and some do not.

The structure is:

• láta
  • infinitive + object

So:

• láta klippa hárið
• literally something like cause/arrange [someone] to cut the hair
• idiomatically have the hair cut

The doer of the action is left unspoken. If needed, Icelandic can mention the person, but in everyday service situations it is very normal to leave them out.

With body parts and things closely connected to the person, Icelandic often uses the definite form alone where English prefers a possessive.

So láta klippa hárið naturally means have my hair cut in this context, even though my is not said explicitly.

English says:

• I’m washing my hands
• I cut my hair

Icelandic very often prefers the equivalent of:

• I’m washing the hands
• I cut the hair

when the owner is already obvious.

They are the direct objects of klippa, laga, and stytta, so they are in the accusative.

• klippa hárið
• laga lásinn
• stytta faldinn

In these particular nouns, the accusative form looks the same as the nominative form, so you do not see a visible difference here. But grammatically they are objects in the accusative.

Because the speaker means specific things:

• the hair belonging to the speaker
• the lock that needs fixing
• the hem on a particular piece of clothing

In Icelandic, the definite form is very common when the thing is identifiable from context. English sometimes uses a possessive instead, but Icelandic often just uses the definite noun.

Faldur means hem: the folded edge at the bottom of a skirt, dress, trousers, and so on.

So láta stytta faldinn means to have the hem made shorter, usually by a tailor or someone altering clothes.

Sometimes Icelandic can omit repeated words in a list, but repeating láta here is very natural and makes the structure especially clear.

With the repetition, each item clearly means have X done:

• láta klippa hárið
• láta laga lásinn
• láta stytta faldinn

If you remove the later láta, the sentence may still be understandable, but the repeated version is clearer and more balanced.

No. Láta is a very flexible verb. Depending on context, it can mean things like:

• let
• make
• have something done
• leave
• cause

In this sentence, it is the have something done meaning. So it is not really the same as English let here, even though dictionaries often list let as one meaning.