Moj brat nikad ne sluša muziku u sobi.

Because moj must agree with the noun it describes.

• brat = brother
• brat is masculine singular
• so the correct form is moj = my for masculine singular nouns

Compare:

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

So moj brat is the correct masculine form.

Yes, it is a double negative, but that is normal and required in Serbian.

In Serbian, when you use a negative word like nikad (never), the verb is also normally negated with ne:

• Nikad ne sluša = He never listens

This is different from standard English, where double negatives are usually avoided.

Other examples:

• Nikad ne idem tamo. = I never go there.
• Niko ne zna. = Nobody knows.
• Ništa ne vidim. = I see nothing / I don’t see anything.

So nikad ne is exactly what you should expect.

In Serbian, the negative particle ne is usually written as a separate word before the verb:

• sluša = listens
• ne sluša = does not listen

So:

• On sluša muziku. = He listens to music.
• On ne sluša muziku. = He does not listen to music.

A few verbs behave differently and form one written word with ne, but with most verbs, including slušati, it stays separate.

Sluša is the 3rd person singular present tense of slušati (to listen).

The subject is moj brat = my brother, which is he, so Serbian uses the 3rd person singular form.

A few present-tense forms of slušati:

• ja slušam = I listen
• ti slušaš = you listen
• on/ona/ono sluša = he/she/it listens
• mi slušamo = we listen
• vi slušate = you (plural/formal) listen
• oni/one/ona slušaju = they listen

So moj brat ... sluša matches correctly.

Because muziku is the accusative singular form of muzika.

The verb slušati usually takes a direct object, and direct objects are commonly in the accusative case.

• muzika = music (nominative)
• muziku = music (accusative)

So:

• Muzika je glasna. = The music is loud.
  Here muzika is the subject, so nominative.
• Sluša muziku. = He/she listens to music.
  Here muziku is the object, so accusative.

This is a very common pattern in Serbian.

Because u sobi uses the locative case and means in the room as a location.

With u, Serbian often uses:

• locative for location: where?
• accusative for direction/movement toward: where to?

So:

• u sobi = in the room (location)
• u sobu = into the room (movement)

Compare:

• Moj brat sluša muziku u sobi. = My brother listens to music in the room.
• Moj brat ulazi u sobu. = My brother is entering the room.

Since this sentence describes where he listens, not movement into the room, u sobi is correct.

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

The neutral sentence is:

• Moj brat nikad ne sluša muziku u sobi.

But you could also hear:

• Moj brat u sobi nikad ne sluša muziku.
• Nikad moj brat ne sluša muziku u sobi.
• Muziku moj brat nikad ne sluša u sobi.

These alternatives shift the emphasis a bit.

A useful thing to remember is that ne stays with the verb, so ne sluša should stay together as a negative verb phrase.

Yes, and in fact that is what happens here.

Serbian often drops subject pronouns when the meaning is already clear from the verb form or from the noun phrase.

Instead of saying:

• On nikad ne sluša muziku u sobi. = He never listens to music in the room.

the sentence uses the noun phrase directly:

• Moj brat nikad ne sluša muziku u sobi.

If the subject were already known, Serbian could even just say:

• Nikad ne sluša muziku u sobi. = He/She never listens to music in the room.

The verb form and context often make the subject clear enough.

In most everyday contexts, nikad means never.

You may also see nikada, which means the same thing. Nikad is just the shorter, very common form.

So:

• nikad = never
• nikada = never

Examples:

• Nikad ne kasnim.
• Nikada ne kasnim.

Both mean I’m never late.

The shorter form nikad is extremely common in speech.

No. Slušati usually means to listen (to), not to hear.

That distinction is important:

• slušati = to listen
• čuti = to hear

So:

• Slušam muziku. = I’m listening to music.
• Čujem muziku. = I hear music.

In your sentence, ne sluša muziku means he does not listen to music, not that he cannot hear it.

Most naturally, it means:

My brother never listens to music in the room.

So the phrase u sobi limits the statement to that location.

In other words, the sentence most strongly suggests that the never applies to listening to music in the room. He might still listen to music somewhere else.

If you wanted to emphasize that he never listens to music anywhere, Serbian would usually express that differently, for example without the location phrase, or with a broader context.

Yes, if the context already makes it clear what he does or does not listen to.

For example:

• Moj brat nikad ne sluša u sobi.

Grammatically, this is possible, but it sounds incomplete unless the listener already knows what is being talked about.

Because slušati often expects an object, muziku makes the sentence much more natural and complete here.

So in this sentence, keeping muziku is the normal choice.