Ako ti muzika smeta, televizor može da radi tiho.

Because the verb smetati takes the person affected in the dative case, not the accusative.

• ti = to you / you in the dative
• tebe would be a different case and would not fit here

So:

• Muzika ti smeta. = The music bothers you.

This is a very common Serbian pattern: the thing causing annoyance is the subject, and the person who feels bothered is in the dative.

Because muzika is the subject of smeta.

In Serbian, with smetati, the structure is usually:

• something
  • smeta
    • someone in dative

So literally the grammar is like:

• Music bothers you

That is why:

• muzika = nominative subject
• ti = dative indirect object / experiencer

Not:

• muziku — that would be accusative, and it would not work in this sentence

Smetati means things like:

• to bother
• to disturb
• to be a nuisance
• to annoy
• sometimes to be in the way

Its most common pattern is:

• X smeta nekome
• Something bothers someone

Examples:

• Dim mi smeta. = The smoke bothers me.
• Buka im smeta. = The noise bothers them.

So in your sentence, muzika smeta means the music is what is causing the problem.

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

So after Ako, the clitic ti comes very early:

• Ako ti muzika smeta...

This is very natural Serbian word order.

You may also hear:

• Ako ti smeta muzika...

That is also natural, because ti still stays near the beginning as a clitic.

But Ako muzika ti smeta sounds wrong or at least very unnatural.

Yes. That is completely natural.

Both of these work:

• Ako ti muzika smeta, ...
• Ako ti smeta muzika, ...

The difference is mostly focus or rhythm:

• Ako ti muzika smeta... gives a bit more prominence to muzika
• Ako ti smeta muzika... is also very common and often sounds slightly more conversational

Both mean the same thing.

In modern Serbian, after modal verbs like moći, it is very common to use:

• može da + present tense

So:

• može da radi

This is one of the most standard ways to say can work / can be on / can run.

You may also encounter an infinitive in some contexts:

• može raditi

But može da radi is extremely common and very natural in everyday Serbian.

In Serbian, raditi is often used for machines and devices to mean:

• to work
• to operate
• to be on
• to run

So for a TV, radio, air conditioner, washing machine, etc., radi is completely normal.

Examples:

• Televizor radi. = The TV is on / working.
• Radio radi tiho. = The radio is on quietly.

So here televizor može da radi tiho means the TV can stay on, but at a low volume.

Because tiho is an adverb, not an adjective.

Here it describes how the TV is operating:

• radi tiho = works / plays quietly

Compare:

• tih televizor = a quiet TV → adjective describing the noun
• televizor radi tiho = the TV works quietly → adverb describing the verb

So tiho is the correct form here.

Televizor is in the nominative singular because it is the subject of može da radi.

In the second clause:

• televizor = subject
• može da radi = predicate
• tiho = adverb

So the structure is:

• The TV can operate quietly

Because the sentence begins with a conditional clause introduced by ako:

• Ako ti muzika smeta, ...
• If the music bothers you, ...

After that introductory clause, Serbian normally uses a comma before the main clause:

• ..., televizor može da radi tiho.

This is similar to English punctuation in sentences like:

• If the music bothers you, the TV can stay on quietly.

Usually, yes. Ako is the normal Serbian word for if in conditional sentences.

Examples:

• Ako dođe, javi mi. = If he comes, let me know.
• Ako hoćeš, možemo krenuti. = If you want, we can leave.

So in your sentence, ako introduces the condition under which the suggestion in the second clause applies.

Because Serbian often uses the present tense in general statements, conditions, and practical suggestions.

Here the sentence is not about a specific past or future event. It expresses a general present situation:

• If the music bothers you, the TV can be on quietly.

Also, both verbs are imperfective, which fits ongoing states or actions:

• smetati = to be bothering / to bother
• raditi = to work / run / be operating

That makes them natural here.

Yes, it is natural. A native speaker could say exactly this.

Some close alternatives are also possible, for example:

• Ako ti smeta muzika, televizor može da radi tiho.
• Ako ti muzika smeta, TV može da radi tiho.
• Ako ti smeta muzika, televizor može biti utišan.

But your original sentence is perfectly normal and idiomatic.