Ég ætla að láta stytta kjólinn minn fyrir brúðkaupið.

Icelandic does not have a separate future tense ending like English will. A very common way to talk about the future is ætla að + infinitive, which means intend to, plan to, or be going to.

So Ég ætla að... means the speaker has the intention or plan to do this.

Here láta is being used in a causative sense. That means it expresses having something done rather than doing it yourself.

So láta stytta kjólinn minn means have my dress shortened. The speaker is arranging for the shortening to happen, probably by someone else such as a tailor or seamstress.

Because those two verbs behave differently.

• ætla normally takes að + infinitive:
  ætla að fara, ætla að gera
• láta in the causative construction takes a bare infinitive:
  láta laga, láta þrífa, láta stytta

So the structure is:

ég ætla að + láta + stytta

not ég ætla að láta að stytta

Stytta is the infinitive form of the verb stytta, meaning to shorten.

After causative láta, Icelandic uses the infinitive, so láta stytta means have someone shorten.

With clothing, stytta often means shortening the length of something, so in practice it can be close to English hem or take up, depending on context.

Kjólinn minn is the normal, neutral everyday way to say my dress when talking about a specific dress.

Icelandic very often uses this pattern:

noun + definite article + possessive

For example:

• bíllinn minn = my car
• húsið mitt = my house
• kjólinn minn = my dress

A form like minn kjóll is possible, but it usually sounds more emphatic, contrastive, or stylistically marked, something like my dress as opposed to someone else’s.

Because the sentence is referring to a particular dress, not just any dress.

In Icelandic, the definite article is usually attached to the end of the noun:

• kjóll = a dress
• kjólinn = the dress

When followed by a possessive like minn, this often corresponds to English my dress.

It is in the accusative, because it is the object of stytta: the dress is the thing being shortened.

The possessive minn agrees with the noun in gender, number, and case, so it matches kjólinn.

In this sentence, fyrir is a preposition of time meaning before.

So:

fyrir brúðkaupið = before the wedding

This is one of several meanings of fyrir. In other contexts it can mean things like for, in front of, or on behalf of. Prepositions in Icelandic often have several meanings, so context is very important.

Brúðkaup is a neuter noun meaning wedding. Here it is definite singular:

• brúðkaup = a wedding
• brúðkaupið = the wedding

After fyrir meaning before in a time expression, Icelandic uses the accusative. For this noun, the nominative and accusative singular definite forms look the same, so you still see brúðkaupið.

Yes, that is the usual implication.

Láta + infinitive often means that the subject causes or arranges for the action to be done, rather than doing it personally.

So this sentence naturally suggests something like:

• taking the dress to a tailor
• asking a seamstress to alter it
• arranging for someone to shorten it

If you want to mention the person, you can:

Ég ætla að láta saumakonu stytta kjólinn minn.
I’m going to have a seamstress shorten my dress.

Yes. Icelandic word order is more flexible than English, especially with time phrases like fyrir brúðkaupið.

The original order is natural and neutral:

Ég ætla að láta stytta kjólinn minn fyrir brúðkaupið.

But you could also say:

Fyrir brúðkaupið ætla ég að láta stytta kjólinn minn.

That version puts more emphasis on before the wedding. The meaning stays basically the same.