Ja sada čitam knjigu, a moja sestra sluša muziku.

Yes. Serbian often drops subject pronouns because the verb ending usually already shows who is doing the action.

• čitam = I am reading / I read
• sluša = he/she is listening

So Ja sada čitam knjigu could also be just Sada čitam knjigu.

The pronoun ja is often used for:

• emphasis: I am reading
• contrast: I am reading, but my sister is listening to music
• clarity, if needed

In this sentence, ja sounds natural because it contrasts nicely with moja sestra.

Sada means now.

In Serbian, adverbs like sada can often move around more freely than in English. For example:

• Ja sada čitam knjigu.
• Sada čitam knjigu.
• Ja čitam knjigu sada.

All are possible, though they may sound slightly different in emphasis.

In your sentence, ja sada čitam knjigu is a very natural way to say I am reading a book now / I am now reading a book.

Čitam is the present tense of čitati (to read).

Serbian usually uses the simple present tense where English might use either:

• I read
• I am reading

So čitam can mean:

• I read
• I am reading

Because sada means now, the meaning is clearly I am reading now.

By contrast, sam čitao is a past-tense form:

• čitao sam = I was reading / I read (masculine speaker)
• čitala sam = I was reading / I read (feminine speaker)

Because it is the direct object of the verb čitati.

The noun knjiga is in the nominative form, which is the basic dictionary form:

• knjiga = book

But after a transitive verb like čitati (to read), the direct object usually goes into the accusative:

• čitam knjigu = I am reading a book

So:

• knjiga = nominative
• knjigu = accusative

This is a very important Serbian pattern:

• Vidim sestru. = I see my sister.
• Imam knjigu. = I have a book.
• Čitam knjigu. = I am reading a book.

For the same reason as knjigu: muziku is the accusative form, used for the direct object.

• muzika = nominative
• muziku = accusative

Since slušati (to listen to) takes a direct object in Serbian, you say:

• slušam muziku = I listen to music / I am listening to music

This is different from English, where we usually say listen to music with the preposition to. Serbian does not use a preposition here.

Because Serbian and English handle this verb differently.

In English:

• listen to music

In Serbian:

• slušati muziku

The Serbian verb slušati takes a direct object, so no preposition is needed.

Compare:

• slušam radio = I listen to the radio
• sluša pesmu = he/she is listening to a song
• slušamo profesora = we are listening to the professor

So this is something English speakers simply need to learn as a verb pattern:

• slušati + accusative

Both a and i can sometimes be translated as and, but they are not used in exactly the same way.

• i usually simply adds one thing to another: and
• a often links two ideas with a slight sense of contrast, switch of topic, or whereas

In this sentence:

• Ja sada čitam knjigu, a moja sestra sluša muziku.

The idea is:

• I am reading a book, while / and meanwhile my sister is listening to music.

So a is a good choice because it sets up a comparison or contrast between what two different people are doing.

If you used i, it would sound more like simple addition:

• Ja sada čitam knjigu i moja sestra sluša muziku.

That is possible in some contexts, but a is more natural here.

Both are possible.

• moja sestra = my sister
• sestra = sister / the sister, depending on context

Serbian often uses possessive adjectives like moj, moja, moje when it wants to be clear whose person or thing is meant.

Here, moja sestra is natural because it clearly means my sister and balances well with ja.

Also notice agreement:

• moj for masculine nouns
• moja for feminine nouns
• moje for neuter nouns

Since sestra is feminine, you use moja.

Because it must agree with the noun sestra, which is feminine singular.

In Serbian, possessive words like moj change form to match the noun they describe.

Examples:

• moj brat = my brother
• moja sestra = my sister
• moje dete = my child

So moja is the correct form because sestra is feminine.

Serbian verb endings usually tell you the person and number.

For čitati in the present tense:

• čitam = I read / am reading
• čitaš = you read
• čita = he/she/it reads
• čitamo = we read
• čitate = you plural / formal read
• čitaju = they read

For slušati:

• slušam
• slušaš
• sluša
• slušamo
• slušate
• slušaju

So:

• čitam tells you the subject is I
• sluša tells you the subject is he/she/it

That is why Serbian can often omit pronouns.

In isolation, the Serbian present tense can express both:

• an action happening right now
• a habitual action

But in this sentence, sada strongly points to right now:

• Ja sada čitam knjigu = I am reading a book now
• moja sestra sluša muziku = my sister is listening to music

Without sada, čitam knjigu could mean either:

• I am reading a book
• I read books / I read a book, depending on context

Context usually decides the meaning.

It can mean either, depending on context.

Serbian has no articles like English a/an/the, so knjigu by itself does not tell you whether it is:

• a book
• the book

The listener understands this from context.

So:

• Čitam knjigu. can mean I am reading a book or I am reading the book.

In learner translations, it is often rendered as a book if nothing specific has been mentioned before.

Serbian word order is more flexible than English word order, although some versions sound more natural than others depending on emphasis.

Possible variations include:

• Ja sada čitam knjigu, a moja sestra sluša muziku.
• Sada čitam knjigu, a moja sestra sluša muziku.
• Knjigu sada čitam, a moja sestra sluša muziku.
  This gives special emphasis to knjigu.
• Moja sestra sluša muziku, a ja sada čitam knjigu.
  This changes what comes first in the discourse.

The most neutral version is close to the one you were given.

A rough pronunciation guide:

• čitam ≈ CHEE-tahm
• sluša ≈ SLOO-shah

A few helpful sound notes:

• č sounds like ch in chocolate
• š sounds like sh in shoe
• c in sada is not present, but if you see c elsewhere in Serbian, it sounds like ts
• j in Serbian sounds like English y in yes

Also:

• ja ≈ yah
• knjigu is a bit tricky because of knj; roughly KNYEE-goo
• muziku ≈ MOO-zee-koo

Yes, both čitati and slušati are imperfective verbs.

That matters because imperfective verbs are commonly used for:

• ongoing actions
• repeated actions
• general processes

So in this sentence, imperfective aspect fits perfectly:

• čitam = I am in the process of reading
• sluša = she is in the process of listening

If Serbian wanted to express a completed action, it would normally use a perfective verb in a different context, usually not in the plain present tense for ordinary present-time actions.

For a beginner, the key point is:

• čitati and slušati are the normal choices for reading/listening right now.

Yes, you can.

• Čitam knjigu, a moja sestra sluša muziku.

This can still mean I am reading a book, and my sister is listening to music, especially if the situation already makes it clear that both actions are happening now.

Adding sada just makes the time reference more explicit:

• right now
• at the moment

So sada is helpful, but not always necessary.