Какую музыку ты любишь слушать вечером?

Because какую has to agree with музыку.

• музыка is feminine
• here it is in the accusative singular
• so какой changes to какую

So:

• nominative: какая музыка = what music
• accusative: какую музыку = what music as the object of the verb

In this sentence, music is the thing being listened to, so Russian uses the accusative form.

For the same reason: музыка is the direct object of слушать.

In Russian, direct objects usually go in the accusative case.
So:

• музыка = nominative
• музыку = accusative

Compare:

• Музыка красивая. = The music is beautiful.
• Я люблю музыку. = I love music.

In your sentence, the speaker is asking about the music someone likes to listen to, so музыку is required.

This is how Russian says like to do something.

• любишь = you like / you love
• слушать = to listen

Together, любишь слушать means like to listen.

This is very similar to English:

• You like listening to music
• You like to listen to music

Russian often uses любить + infinitive to express liking an activity:

• Я люблю читать. = I like reading / I like to read.
• Он любит гулять. = He likes walking.

Because after любить in this meaning, Russian normally uses the infinitive.

So:

• ты любишь слушать = you like to listen
• not ты любишь слушаешь

That would be like saying in English you like you listen, which does not work.

The first verb is the main verb and is conjugated:

• люблю, любишь, любит...

The second verb stays in the infinitive:

• слушать

Вечером is a very common Russian adverbial form meaning in the evening.

It comes from вечер but appears in the instrumental case:

• утром = in the morning
• днём = in the daytime
• вечером = in the evening
• ночью = at night

So вечером functions almost like an adverb here.

You do not say в вечером.
If you use в, you would need a different structure, for example:

• в этот вечер = on this evening
• вечером = in the evening / during the evening

Usually it means what kind of music.

In English, What music do you like? often really means What kind of music do you like?
Russian works the same way here.

So Какую музыку ты любишь слушать вечером? is asking about genre, style, or type, for example:

• джаз
• рок
• классическую музыку
• спокойную музыку

Depending on context, it can also mean which music, but most of the time it is understood as what kind of music.

Yes. Russian often leaves out subject pronouns when they are clear from the verb ending.

So both are natural:

• Какую музыку ты любишь слушать вечером?
• Какую музыку любишь слушать вечером?

Because любишь already tells you the subject is you singular.

Including ты can make the sentence:

• a little clearer
• a little more personal
• slightly more emphatic, depending on context

No, Russian word order is fairly flexible, though some orders sound more neutral than others.

The given sentence is a normal, neutral way to ask the question:

• Какую музыку ты любишь слушать вечером?

But other orders are possible, with different emphasis:

• Ты какую музыку любишь слушать вечером?
  This can put extra focus on what music
• Вечером какую музыку ты любишь слушать?
  This highlights in the evening

Russian often moves words around for emphasis, topic, or style.
Still, question words like какую very often appear near the beginning.

Because слушать is imperfective, and that fits a general or habitual idea.

The sentence is asking about someone's usual preference:

• What music do you like to listen to in the evening?

That is a repeated, ongoing habit, so слушать is the natural choice.

Послушать is perfective and usually suggests:

• listening once
• listening for a while
• listening to something as a completed action

So любишь слушать = like listening / like to listen in general.
That is why слушать is better here.

Replace ты with вы, and change the verb accordingly:

• Какую музыку вы любите слушать вечером?

This is the polite or plural form.

So:

• ты любишь = singular informal
• вы любите = plural or polite singular

Russian uses вы the way English uses polite you, especially with strangers, older people, teachers, customers, and in formal situations.