Ég vil ekki sleppa morgunmatnum í dag.

Vilja is the dictionary form, meaning to want. In the sentence, the verb has to match ég (I), so it becomes vil, the 1st person singular present form.

This verb is irregular, so its present-tense forms are worth memorizing:

• ég vil — I want
• þú vilt — you want
• hann/hún/það vill — he/she/it wants

So Ég vil simply means I want.

Because vilja normally takes a bare infinitive in Icelandic.

So you say:

• Ég vil fara — I want to go
• Ég vil borða — I want to eat
• Ég vil ekki sleppa — I do not want to skip

English uses to after want, but Icelandic does not use að here.

Yes — sleppa has several related meanings, and this is very common in Icelandic.

Depending on context, sleppa can mean things like:

• let go / release
• get away / escape
• avoid / go without
• skip / leave out

In this sentence, it means skip:

• sleppa morgunmatnum — skip breakfast

So this is a normal, idiomatic use of the verb.

Because vil is the finite verb, and in a normal Icelandic main clause the finite verb usually comes early in the sentence. The negative word ekki normally comes after that finite verb.

So the structure is:

• Ég — subject
• vil — finite verb
• ekki — not
• sleppa — infinitive
• morgunmatnum — object
• í dag — today

That is why Ég vil ekki sleppa... is natural, while putting ekki before vil would not be the normal pattern here.

Because sleppa in the sense of skip takes a dative object.

The basic noun is morgunmatur — breakfast.

But after sleppa, it appears in the dative singular definite form:

• morgunmatur — breakfast
• morgunmatinn — the breakfast, accusative
• morgunmatnum — the breakfast, dative

So:

• sleppa morgunmatnum = skip breakfast

This is an important Icelandic pattern: not every direct object is accusative. Some verbs govern dative, and sleppa is one of them in this meaning.

Because Icelandic and English do not use the definite article in exactly the same way.

English often says:

• skip breakfast
• eat lunch
• after dinner

with no article.

Icelandic often prefers a definite form when referring to the specific meal in question, especially a meal connected to a particular day or situation:

• morgunmatnum — literally the breakfast

Here it refers naturally to today’s breakfast / the breakfast I would normally have today. English usually leaves the article out, but Icelandic often does not.

The dictionary form is morgunmatur.

In this sentence, that noun has changed form because of case and definiteness.

A useful mini-pattern is:

• morgunmatur — breakfast
• morgunmat — breakfast, accusative/dative stem form without article
• morgunmatnum — the breakfast, dative singular definite

So -num here is part of the dative definite ending. Icelandic often adds the definite article to the end of the noun instead of using a separate word like English the.

Literally, í dag is in day, but as a fixed Icelandic expression it simply means today.

This is one of the most common time expressions in the language:

• í dag — today
• í gær — yesterday
• á morgun — tomorrow

So even though í often means in, you should learn í dag as a whole phrase meaning today.

Because dagur is the dictionary form, but after í in this fixed expression the noun appears as dag.

So:

• dagur — day
• í dag — today

You do not need to analyze this too heavily every time; for learners, it is best to memorize í dag as a set phrase.

Yes. Icelandic word order is flexible, and fronting a time expression is very common.

You can say:

• Ég vil ekki sleppa morgunmatnum í dag.
• Í dag vil ég ekki sleppa morgunmatnum.

Both are natural.

The difference is mainly emphasis:

• Ég vil ekki sleppa morgunmatnum í dag is a neutral statement.
• Í dag vil ég ekki sleppa morgunmatnum puts extra focus on today.

Notice that when Í dag moves to the front, the finite verb vil still stays in the second position. That is a classic Icelandic V2 pattern.

In normal English translation, it is best understood as I don’t want to skip...

Grammatically, Icelandic has:

• vil — want
• ekki — not
• sleppa — skip

But in natural usage, vil ekki + infinitive is simply the normal way to say do not want to do something:

• Ég vil ekki fara — I don’t want to go
• Ég vil ekki borða — I don’t want to eat
• Ég vil ekki sleppa morgunmatnum — I don’t want to skip breakfast

So you should treat vil ekki as a very common pattern meaning don’t want to.