Privremeni odlazak može trajati godinu dana.

Because it agrees with odlazak.

• odlazak is a masculine singular noun
• here it is in the nominative singular
• the adjective has to match it in gender, number, and case

So:

• privremeni odlazak = masculine singular nominative

If the noun changed, the adjective would change too, for example:

• privremena odsutnost = temporary absence
• privremeno rješenje = temporary solution

No, odlazak is a noun.

It means departure, leaving, or going away.

It is related to the verb family of odlaziti / otići:

• odlaziti = to be leaving / to go away regularly or in progress
• otići = to leave, to go away
• odlazak = departure / leaving

So in this sentence, Croatian uses a noun where English might also use a noun: temporary departure.

Because može is the 3rd person singular of moći = can / may / be able to, and after a modal verb Croatian normally uses the infinitive.

So:

• može = can / may
• trajati = to last

Together:

• može trajati = can last / may last

This is very normal Croatian structure.

Because after može, Croatian uses the infinitive, not another finite verb form.

Compare:

• Traje godinu dana. = It lasts a year.
• Može trajati godinu dana. = It can last a year.

So:

• traje = present tense, it lasts
• trajati = infinitive, to last

It can suggest either, depending on context.

In a sentence like this, može often means:

• can = it is possible
• may = it is allowed / permitted
• sometimes even can be up to in administrative language

Because privremeni odlazak sounds a bit formal or official, the sentence may be understood as something like:

• a temporary departure may/can last one year
• a temporary departure is allowed to last one year
• a temporary departure can be for up to one year

The exact nuance depends on the larger context.

This is the normal Croatian way to express a duration like a year.

• godinu is the accusative singular of godina
• dana is part of the fixed time expression godinu dana

So:

• trajati godinu dana = to last a year

This is more idiomatic than simply using jednu godinu in most everyday situations.

Godinu is in the accusative singular.

Croatian often uses the accusative to express duration of time:

• čekam sat vremena = I’m waiting for an hour
• radio je cijeli dan = he worked all day
• trajati godinu dana = to last a year

So here the duration how long? is expressed with the accusative.

In godinu dana, dana is part of a very common idiomatic time expression.

Literally, it looks a bit like a year of days, but you should learn it as a set phrase meaning:

• a year
• for a year
• lasting a year

Similar patterns exist with other time expressions, for example:

• mjesec dana = a month
• tjedan dana = a week
• par dana = a couple of days

So godinu dana is best treated as a natural Croatian chunk.

Yes, it is possible, but godinu dana is usually more natural here.

Compare:

• može trajati godinu dana = the usual, idiomatic way
• može trajati jednu godinu = understandable, but more marked or less natural in many contexts

A learner will sound more natural using godinu dana for duration.

No, Croatian word order is fairly flexible, but this version is the most neutral and natural:

• Privremeni odlazak može trajati godinu dana.

You may see other orders for emphasis, but they are less neutral, for example:

• Godinu dana može trajati privremeni odlazak.
• Privremeni odlazak godinu dana može trajati.

Those are possible, but the original sentence is the safest standard order for learners.

Because Croatian has no articles.

English uses:

• a temporary departure
• the temporary departure

Croatian usually expresses that meaning without articles:

• privremeni odlazak

Whether it means a temporary departure or the temporary departure depends on context.

Yes, but it sounds a bit formal or administrative.

It is the kind of phrase you might see in:

• official rules
• legal or bureaucratic texts
• workplace or residence documents

In more casual speech, people might more often use a verb phrase instead, such as:

• privremeno otići = to leave temporarily
• biti odsutan neko vrijeme = to be away for some time

So the sentence is natural, but it has a somewhat official tone.