Ég tek snarlið með mér í vinnuna.

Tek is the 1st person singular present form of the verb taka (to take).

So:

• að taka = to take
• ég tek = I take

This verb is a bit irregular, so the present tense does not simply look like taka plus an ending. That is why tek may seem quite different at first.

A few useful present-tense forms are:

• ég tek = I take
• þú tekur = you take
• hann/hún/það tekur = he/she/it takes

In this sentence, ég tek can often be understood naturally as I take / I’m taking depending on context.

Literally, tek means take. But in a sentence like this, English often prefers bring.

That is because Icelandic commonly says take X with me where English might say bring X with me.

So:

• Ég tek snarlið með mér í vinnuna
  literally: I take the snack with me to work
• natural English: I bring the snack with me to work

This is very normal Icelandic usage.

Snarlið is the definite singular form of snarl.

• snarl = snack, light food, something quick to eat
• snarlið = the snack

It is a neuter noun.

In this sentence, it is the thing being taken, so it functions as the direct object.

Because snarlið has the definite article attached to the end.

Icelandic usually adds the as a suffix rather than writing it as a separate word.

So:

• snarl = a snack / snack
• snarlið = the snack

This is a very important Icelandic pattern. The same thing also happens in vinnuna later in the sentence.

Because með (with) takes the dative case here, and the dative form of ég is mér.

The relevant forms are:

• ég = I
• mig = me (accusative)
• mér = me (dative)
• mín = my/mine in certain forms

So:

• með mér = with me

You cannot say með ég, because ég is the subject form, not the form used after this preposition.

Yes. A very useful pattern is:

• taka eitthvað með sér = to take something with oneself / to take something along

In dictionary-style explanations, you will often see með sér. But that changes depending on the person:

• ég tek ... með mér = I take ... with me
• þú tekur ... með þér = you take ... with you
• hann tekur ... með sér = he takes ... with him

So in your sentence, með mér is exactly what you expect with a 1st person singular subject.

Because Icelandic uses:

• í + accusative for motion toward / into
• í + dative for location in

So:

• í vinnuna = to work / into work / to the workplace
• í vinnunni = at work / in the workplace

That is a very common and important contrast in Icelandic.

Compare:

• Ég fer í vinnuna. = I go to work.
• Ég er í vinnunni. = I am at work.

In your sentence, there is movement toward work, so accusative is used: vinnuna.

Because Icelandic and English do not always use definiteness in the same way.

• vinna = work
• vinnan = the work
• vinnuna = the work (accusative singular)

In expressions like í vinnuna, Icelandic often uses the definite form where English simply says to work.

So even though vinnuna literally looks like the work, the natural translation is often just:

• to work

This is something learners just get used to over time.

This is the most neutral order:

• Ég tek snarlið með mér í vinnuna.

But Icelandic word order can change for emphasis, topic, or style.

For example, you could move another element to the front, but then the finite verb still normally stays in second position in a main clause:

• Snarlið tek ég með mér í vinnuna.
  = The snack, I’m taking with me to work.

That sounds more marked or contrastive. The original version is the most straightforward everyday wording.

A rough pronunciation guide is:

yeg tek SNAR-lith meth myair ee VINN-oo-na

A few notes:

• Ég sounds roughly like yeg, though the real Icelandic sound is not exactly like English.
• snarlið ends in -ið, where ð is like a soft th sound in this, though it can be very light.
• með also has ð, again a soft th-type sound.
• mér is roughly like myair.
• vinnuna has stress on the first syllable: VINN-oo-na.

As in most Icelandic words, the main stress is usually on the first syllable.