Þú lítur mjög þreytt út.

Yes. Líta út is a very common Icelandic expression meaning to look / to appear / to seem.

So in this sentence, lítur ... út works together as a unit:

• Þú lítur ... út = you look / you appear

It is not the same as English look out.

Lítur is the present tense, 2nd person singular form of the verb líta.

A few present-tense forms are:

• ég lít = I look
• þú lítur = you look
• hann/hún/það lítur = he/she/it looks

So Þú lítur simply means you look.

Because líta út is a verb + particle expression, and in Icelandic the particle is often separated from the main verb.

In this kind of sentence, the normal pattern is:

• líta + description + út

So:

• Þú lítur mjög þreytt út

That is more natural than putting út directly after lítur here.

Because adjectives in Icelandic must agree with the person they describe in gender, number, and case.

Here, þreytt is the form you would normally use when speaking to one woman/girl:

• Þú lítur mjög þreytt út.

If you were speaking to one man/boy, you would usually say:

• Þú lítur mjög þreyttur út.

So the sentence as written is most naturally addressed to a female person.

It is in the nominative, because it is a predicate adjective describing the subject þú.

This is similar to how adjectives behave after verbs like:

• vera = to be
• verða = to become
• líta út = to look/appear

So the adjective agrees with the subject, rather than acting like a direct object.

Mjög means very.

It is an adverb, and here it modifies the adjective þreytt:

• mjög þreytt = very tired

Its normal place is before the adjective or adverb it strengthens.

The letter þ is pronounced like th in thing, not like th in this.

So:

• þú is roughly thoo

Also:

• ú sounds like oo in food

So Þú is approximately thoo.

Þú is the normal singular word for you in modern Icelandic.

Unlike some European languages, Icelandic does not usually use a separate formal you in everyday modern speech. So þú is standard even in many polite situations.

Yes.

• Þú ert mjög þreytt/þreyttur. = You are very tired.
• Þú lítur mjög þreytt út. = You look very tired.

The difference is:

• ert says the person is tired
• lítur ... út says the person looks/seems tired

So líta út is a bit less direct and more about appearance.

Normally, you should include it.

Icelandic usually keeps subject pronouns in ordinary sentences, so:

• Þú lítur mjög þreytt út.

is the normal full sentence.

Unlike languages such as Spanish or Italian, Icelandic does not regularly leave the subject pronoun out.

For a yes/no question, Icelandic typically puts the verb first:

• Lítur þú mjög þreytt út? = Do you look very tired?

So the statement:

• Þú lítur mjög þreytt út.

becomes:

• Lítur þú mjög þreytt út?

A little, but the sentence you have is the most natural neutral order:

• Þú lítur mjög þreytt út.

Because mjög þreytt belongs together as the description, it normally stays before út.

More unusual word orders are possible in special contexts, but for a learner, the safest pattern is:

• subject + líta + adverb + adjective + út