Kupac proverava kilometražu i servisnu knjižicu.

Because they are direct objects of the verb proverava.

In Serbian, feminine nouns ending in -a usually change to -u in the accusative singular:

• kilometraža → kilometražu
• knjižica → knjižicu

The adjective also has to match the noun, so:

• servisna knjižica → servisnu knjižicu

So the sentence uses the accusative because the buyer is checking what?

• the mileage
• the service booklet

Kupac is in the nominative singular, because it is the subject of the sentence.

It is the person doing the action:

• Kupac = the buyer
• proverava = checks

So kupac is the one who checks something.

Proverava is the 3rd person singular present tense of the imperfective verb proveravati / proveravati? In standard usage here, the base verb is usually understood as proveravati or the present of proveriti/proveravati patterns depending on teaching tradition, but in this sentence proverava simply means is checking / checks.

For learners, the important point is:

• proverava = he/she/it checks, or is checking
• it matches the singular subject kupac

By contrast, proveri is usually associated with:

• imperative: check!
• or forms related to the perfective verb in other constructions

So proverava is the natural present-tense form here.

Serbian normally has no articles, so there is no separate word for a or the.

So kupac can mean:

• a buyer
• the buyer

The exact meaning depends on context.

The same is true for:

• servisnu knjižicu = a/the service booklet
• kilometražu = the mileage or just mileage, depending on context

Servisna knjižica is a common expression for a vehicle’s service booklet, service record booklet, or more generally its maintenance record book.

Word by word:

• servisna = service-related
• knjižica = booklet, little book

In car-related contexts, it usually refers to the document showing the vehicle’s service history.

Because adjectives in Serbian must agree with the noun they describe in:

• gender
• number
• case

The noun knjižica is:

• feminine
• singular

In the accusative singular, the adjective changes too:

• nominative: servisna knjižica
• accusative: servisnu knjižicu

So both words shift together.

In this sentence, i means and.

So:

• kilometražu i servisnu knjižicu = the mileage and the service booklet

In other contexts, i can sometimes have an emphatic sense like also/even, but here it is the simple coordinating conjunction and.

Yes. Serbian word order is more flexible than English because case endings show the grammatical roles.

The neutral order here is:

• Kupac proverava kilometražu i servisnu knjižicu.

But other orders are possible, for example:

• Kilometražu i servisnu knjižicu kupac proverava.
• Kupac kilometražu i servisnu knjižicu proverava.

These can sound more marked or emphasize different parts of the sentence. The original version is the most straightforward and natural for a learner.

The letter ž is pronounced like the s in measure or the g in genre.

So:

• kilometražu has that zh sound near the end
• knjižicu also contains the same sound

A rough English-style guide:

• kilometražu ≈ kee-lo-meh-TRA-zhu
• knjižicu ≈ KNYI-zhi-tsu or KNEE-zhi-tsu, depending on how close you get to Serbian pronunciation

Also:

• č is like ch in church
• ć is a softer sound, somewhat like a very soft ty/ch sound

Knjižica is a diminutive form related to knjiga.

• knjiga = book
• knjižica = small book, booklet

So servisna knjižica literally means something like service booklet, not a full-sized book.

Diminutives are very common in Serbian and can indicate:

• smaller size
• a booklet-type object
• sometimes familiarity or affection, depending on context

Because the subject kupac is singular.

• kupac = buyer
• one buyer → singular verb
• therefore: proverava

If the subject were plural, the verb would also be plural:

• Kupci proveravaju kilometražu i servisnu knjižicu.
• The buyers check the mileage and the service booklet.

Yes, kupac is grammatically masculine singular.

It often refers to a male buyer, but in some contexts masculine forms in Serbian can also function in a more general or dictionary-style way. Still, in ordinary usage, if you specifically wanted to refer to a female buyer, you would usually say:

• kupac = male buyer / buyer
• kupkinja = female buyer

In this sentence, kupac is masculine singular and that matches the singular verb proverava.

Yes, depending on nuance.

• proverava = checks, verifies
• pregleda = inspects, looks over, examines

So:

• Kupac proverava kilometražu i servisnu knjižicu. = The buyer is checking/verifying the mileage and the service booklet.

• Kupac pregleda kilometražu i servisnu knjižicu. = The buyer inspects/looks over the mileage and the service booklet.

The original sentence suggests checking the information, not just visually looking at it.