Ég tek brauðsneið með osti þegar ég hef ekki tíma til að elda.

Yes. Tek is the 1st person singular present of taka, which basically means take. In food contexts, though, Icelandic often uses taka the way English might say grab, have, or take something quickly.

So Ég tek brauðsneið með osti suggests something like:

• I grab a slice of bread with cheese
• I have a slice of bread with cheese

If you wanted to focus more directly on eating, you could also use borða:

• Ég borða brauðsneið með osti

The sentence with tek sounds natural if the idea is choosing a quick food option.

Tek is:

• 1st person singular
• present tense
• of the verb taka = to take

So:

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

This is a common irregular verb, so it is worth memorizing.

Because Icelandic very often makes compounds as a single word.

Here:

• brauð = bread
• sneið = slice

Together:

• brauðsneið = slice of bread

This is very normal in Icelandic. English often uses separate words where Icelandic prefers one compound word.

The first part of many Icelandic compounds appears in a genitive-style linking form.

So:

• brauð = bread
• linking/genitive form: brauðs-
• sneið = slice

That gives:

• brauðsneið = literally something like bread's slice, meaning slice of bread

This pattern is very common in Icelandic compounds.

Correct. Icelandic does not have an indefinite article like English a/an.

So:

• brauðsneið can mean a slice of bread
• brauðsneiðin means the slice of bread

The definite article is usually attached to the end of the noun instead of being a separate word.

It is the direct object of tek, so it is in the accusative.

However, the form does not visibly change here. Some Icelandic nouns have the same form in nominative and accusative singular, and brauðsneið is one of those.

So even though the case is accusative, it still looks like brauðsneið.

Because með normally takes the dative when it means with.

The noun is:

• ostur = cheese, nominative
• osti = cheese, dative

So:

• með osti = with cheese

This is something you will see a lot in Icelandic: prepositions often require a specific case.

Yes, that is the natural meaning here.

Brauðsneið með osti means a slice of bread served with cheese on it or as its topping/filling. It works much like English a slice of bread with cheese.

Þegar means when here.

It introduces a subordinate clause:

• þegar ég hef ekki tíma til að elda = when I do not have time to cook

So it connects the two ideas:

• I take a slice of bread with cheese
• when I do not have time to cook

Because þegar introduces a subordinate clause, and subordinate clauses usually keep normal subject + verb order in Icelandic.

So:

• þegar ég hef ekki tíma = when I do not have time

Not:

• þegar hef ég ekki tíma

If you moved the þegar-clause to the front of the whole sentence, then the main clause would change word order:

• Þegar ég hef ekki tíma til að elda, tek ég brauðsneið með osti.

There, tek ég happens because Icelandic main clauses follow the verb-second pattern.

In Icelandic, ekki usually comes after the finite verb.

So:

• ég hef ekki tíma = I do not have time

This is very standard placement:

• ég borða ekki
• hann kemur ekki
• við eigum ekki peninga

So hef ekki is exactly what you should expect.

Because the phrase hafa tíma uses the accusative.

The noun is:

• tími = time, nominative singular
• tíma = time, accusative singular

So:

• ég hef tíma = I have time
• ég hef ekki tíma = I do not have time

This is a very common phrase, so it is useful to learn it as a chunk.

After tími, Icelandic normally uses til að + infinitive to mean time to do something.

So:

• tími til að elda = time to cook
• ég hef ekki tíma til að elda = I do not have time to cook

This is the standard construction.
You can think of til að here as expressing for doing something or in order to do something, though in English we usually just say to.

So this whole part is best learned as:

• hafa tíma til að + infinitive = to have time to do something