Þegar ég er stressaður, er svefninn mikilvægastur.

Þegar means when. It introduces a subordinate time clause:

• Þegar ég er stressaður = When I am stressed

That whole part sets the time or condition for the main statement that follows. In Icelandic, it is very common to put this kind of clause first.

Because the sentence has two clauses, and each clause needs its own finite verb.

• Þegar ég er stressaður → er = am
• er svefninn mikilvægastur → er = is

So this is not repetition by mistake. It is just:

• subordinate clause: I am stressed
• main clause: sleep is most important

This is because of Icelandic verb-second word order in main clauses.

When something else comes first in the sentence — here, the whole clause Þegar ég er stressaður — the finite verb of the main clause usually comes next. So the pattern becomes:

• Þegar ég er stressaður, er svefninn mikilvægastur.

Literally, the order is a bit like:

• When I am stressed, is sleep most important

But in natural English we would say:

• When I am stressed, sleep is most important

So the Icelandic word order is normal and important to learn.

No. Stressaður agrees with the speaker.

Here it is masculine singular nominative, so it would be used by a male speaker saying I am stressed.

Other forms would be:

• masculine: ég er stressaður
• feminine: ég er stressuð

So if a woman is speaking, she would normally say:

• Þegar ég er stressuð, er svefninn mikilvægastur.

It is a loanword, ultimately from English stress, but it is very common in modern Icelandic and behaves like a normal Icelandic adjective.

So even though its origin is foreign, Icelandic still inflects it:

• stressaður
• stressuð
• stressað

That is very common in Icelandic: borrowed words often get fully Icelandic grammar.

Svefninn is the noun svefn with the definite article attached.

• svefn = sleep
• svefninn = the sleep

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

• -inn, -in, -ið, etc.

Here svefninn sounds natural because it refers to sleep as the important thing in the situation being discussed. English often uses a bare noun like sleep, but Icelandic may prefer the definite form in places where English does not.

Mikilvægastur is the superlative form of mikilvægur, meaning most important.

The forms are:

• positive: mikilvægur = important
• comparative: mikilvægari = more important
• superlative: mikilvægastur = most important

So:

• svefninn er mikilvægastur = sleep is most important

That is a very good question. Icelandic adjectives have different forms depending on how they are used.

Here, mikilvægastur is a predicate adjective — it comes after er and describes the subject:

• Svefninn er mikilvægastur.

In this position, Icelandic uses the strong form.

By contrast, mikilvægasti is the form you usually use before a definite noun:

• mikilvægasti hlutinn = the most important part

So compare:

• Svefninn er mikilvægastur. = predicate
• mikilvægasti svefnþátturinn = adjective directly before noun

They are in the nominative here.

• ég is nominative
• stressaður matches ég as a predicate adjective after vera
• svefninn is the subject of the main clause, so it is nominative
• mikilvægastur matches svefninn, so it is also nominative

A useful rule is that with vera = to be, predicate nouns and adjectives are very often in the nominative.

Yes. That is also correct.

Adding þá can make the sentence feel a little more explicit or natural in some contexts:

• Þegar ég er stressaður, þá er svefninn mikilvægastur.

It is a bit like saying:

• When I am stressed, then sleep is most important

In English we usually do not need then, but Icelandic often allows or likes þá after an initial when/if clause.

The comma separates the subordinate clause from the main clause:

• Þegar ég er stressaður, = subordinate clause
• er svefninn mikilvægastur. = main clause

In standard written Icelandic, this comma is normal and helpful. It shows clearly where the first clause ends and the main statement begins.