Moja sestra mi sada vraća knjigu.

Because sestra is a feminine singular noun, and the possessive adjective must agree with it.

So:

• moj = masculine singular
• moja = feminine singular
• moje = neuter singular

Since sestra is feminine, you need moja sestra.

Mi means to me here.

It is the dative singular form of ja. In this sentence, it marks the indirect object: the person who is receiving the book back.

So the structure is roughly:

• moja sestra = subject
• mi = indirect object, to me
• knjigu = direct object, the book

Both can mean to me, but they are used differently.

• mi is the short, unstressed clitic form.
• meni is the full, stressed form.

In a neutral sentence, Serbian usually prefers the short form mi:

• Moja sestra mi sada vraća knjigu.

You would use meni for emphasis or contrast:

• Moja sestra meni sada vraća knjigu, a ne njemu. = My sister is returning the book to me, not to him.

Because knjigu is the accusative singular form of knjiga.

The verb vraćati / vratiti takes a direct object, and direct objects are usually in the accusative.

So:

• knjiga = nominative, dictionary form
• knjigu = accusative, used here because it is the thing being returned

This is very common with feminine nouns ending in -a:

• žena → ženu
• kuća → kuću
• knjiga → knjigu

Vraća is the 3rd person singular present tense form of vraćati.

That matches the subject moja sestra = she / my sister.

So:

• ja vraćam = I return / am returning
• ti vraćaš = you return
• on/ona vraća = he/she returns

Because the subject is sestra, the verb has to be vraća.

This is about aspect, which is very important in Serbian.

• vraćati = imperfective
• vratiti = perfective

In this sentence, vraća is used because the action is presented as happening now or as an ongoing process. The word sada also supports that.

A native English speaker can think of it like this:

• vraća = is returning / returns
• perfective vratiti is more about a completed return

So vraća is the natural choice for right now.

It can technically mean either, because Serbian present tense does not always separate simple present and present progressive the way English does.

But with sada = now, the sentence most naturally means:

• My sister is returning the book to me now.

Without sada, it could also be understood more generally or habitually:

• Moja sestra mi vraća knjigu. = My sister returns / is returning the book to me.

So sada helps make the ongoing, current meaning clearer.

Because Serbian does not have articles like English a and the.

Whether something means a book or the book is understood from context.

So knjigu can mean:

• a book
• the book

In this sentence, context usually makes it clear that it means the book.

Because mi is a clitic, and Serbian clitics usually go in second position in the clause.

That means they tend to come right after the first stressed word or phrase, not just anywhere.

Here the first phrase is Moja sestra, so mi comes right after it:

• Moja sestra mi sada vraća knjigu.

This is much more natural than putting mi later in the sentence.

Yes, Serbian word order is fairly flexible, but not completely free.

You can move words around to change emphasis, for example:

• Sada mi moja sestra vraća knjigu.
• Knjigu mi sada vraća moja sestra.

But the clitic mi still usually stays near the beginning, in its normal clitic position.

So word order can change, but some orders sound much more natural than others.

No, it is not grammatically necessary.

If you remove it, the sentence is still correct:

• Moja sestra mi vraća knjigu.

Adding sada gives a clearer sense of now, at this moment. It helps prevent the sentence from sounding more general or habitual.

So sada is there for time reference and emphasis, not because the grammar requires it.