On je ovaj tjedan zauzet projektom, ali vikendom ima pravo na odmor.

Because je is a clitic form of biti (to be), and Croatian clitics usually go in the second position of the clause.

So:

• On je zauzet. = He is busy.
• not normally On zauzet je.

In your sentence, On is the first element, so je comes right after it.

Yes, very often you can.

Croatian often drops subject pronouns when the meaning is clear from context, so:

• On je ovaj tjedan zauzet projektom...
• Ovaj je tjedan zauzet projektom...
• Ovaj tjedan je zauzet projektom...

can all work, depending on emphasis and style.

Keeping on often adds a bit of contrast or clarity, like he specifically.

Ovaj tjedan means this week.

Here it functions as a time expression, and Croatian often uses the accusative form without a preposition for expressions of time.

A useful point: with tjedan, the nominative and accusative singular look the same:

• nominative: ovaj tjedan
• accusative: ovaj tjedan

So even though the form looks like the basic dictionary form, here it is being used adverbially to mean this week.

You may also see ovog tjedna, which means something like during this week / this week as well. Both are possible, though the nuance and style can differ slightly.

Because the adjective zauzet often takes the instrumental case to express what someone is busy with.

So:

• zauzet projektom = busy with a project
• zauzet poslom = busy with work
• zauzeta djecom = busy with the children

The noun projekt becomes instrumental singular:

• nominative: projekt
• instrumental: projektom

This is a pattern worth memorizing: zauzet + instrumental.

Not always. Zauzet can mean:

• busy
• occupied
• taken
• sometimes even unavailable

depending on context.

In this sentence, zauzet projektom clearly means busy with a project.

Be careful not to confuse it with zaposlen:

• zauzet = busy / occupied
• zaposlen = employed

So On je zauzet means He is busy, not He is employed.

Vikendom is the instrumental singular of vikend, used adverbially.

In Croatian, the instrumental can sometimes express a habitual time meaning, so:

• vikendom = on weekends / at weekends

This usually means something that happens regularly.

Compare:

• vikendom = on weekends, generally/habitually
• za vikend = on the weekend / this weekend / over the weekend, often more specific

So in your sentence, ali vikendom means but on weekends in a general sense.

Because Croatian does not always need a preposition for time expressions.

English says on weekends, but Croatian can simply use the noun in a special case form:

• vikendom
• noću = at night
• danju = by day / during the day

So vikendom is a normal standalone adverbial expression.

Imati pravo na is a very common expression meaning:

• to have the right to
• to be entitled to

So:

• ima pravo na odmor = he has the right to rest
• imam pravo na pauzu = I have the right to a break
• imaju pravo na pomoć = they are entitled to help

This is a fixed pattern, so it is best learned as a chunk:

imati pravo na + accusative

After na in this expression, Croatian uses the accusative.

So:

• pravo na odmor = the right to rest
• pravo na posao = the right to work
• pravo na naknadu = the right to compensation

In this particular noun, odmor, nominative and accusative singular are the same in form, so you do not see a visible change:

• nominative: odmor
• accusative: odmor

But grammatically it is accusative because of na.

Not completely. Croatian word order is fairly flexible, but the emphasis changes, and clitics like je still tend to stay in second position.

For example, you might also hear:

• Ovaj tjedan je zauzet projektom, ali vikendom ima pravo na odmor.
• Projektom je zauzet ovaj tjedan, ali vikendom ima pravo na odmor.

These versions are possible, but they sound different in emphasis. The original sentence is neutral and natural.

So the main idea is:

• word order is flexible
• but not random
• clitic placement still matters

Because Croatian has no articles.

English says:

• this week
• a project
• the right
• a rest / rest

Croatian simply uses the noun without articles:

• ovaj tjedan
• projektom
• pravo
• odmor

Whether something is definite or indefinite is usually understood from context, word order, or other words in the sentence.

It depends on context.

Odmor can mean:

• rest
• time off
• a break
• sometimes holiday/vacation

In this sentence, ima pravo na odmor most naturally means something like:

• has a right to rest
• is entitled to time off

Since the sentence contrasts this week with weekends, the idea is that he is busy now, but weekends are for rest.

Usually, zauzet projektom is the more standard and natural choice for busy with a project.

Zauzet + instrumental is the common pattern.

A phrase like na projektu is possible with some verbs and contexts, for example:

• Radi na projektu. = He is working on a project.

But with zauzet, the expected construction is normally:

• zauzet projektom

So it is best to learn:

• raditi na projektu
• biti zauzet projektom

as two separate patterns.

It breaks down like this:

• On je = He is
• ovaj tjedan = this week
• zauzet projektom = busy with a project
• ali = but
• vikendom = on weekends
• ima pravo na odmor = has the right to rest / is entitled to rest

So the sentence contrasts two time frames:

• this week → he is busy
• on weekends → he has a right to rest

That contrast is carried by ali = but.