Vad är det för musik hon lyssnar på när hon jobbar?

In this sentence, vad är det för means what kind of or what sort of.

So Vad är det för musik ...? is not asking what is music? It is asking about the type of music:

• What kind of music does she listen to when she works?

This is a very common Swedish pattern:

• Vad är det för bok? = What kind of book is it?
• Vad är det för människor? = What kind of people are they?

That is a very common reaction for English speakers. In Swedish, vad är det för ... is an idiomatic structure. The det does not have to be translated word-for-word in normal English.

Literally, it looks a bit like:

• What is it for music ...?

But idiomatically it means:

• What kind of music ...?

So the important thing is to learn vad är det för as a set expression.

Sometimes Swedish uses vilken/vilka for which, but here vad är det för musik is more natural if you are asking about the type/style of music.

Compare:

• Vad är det för musik hon lyssnar på?
  = What kind of music does she listen to?

• Vilken musik hon lyssnar på would sound less natural in this context unless you are choosing from known options or referring to specific music.

So for a broad question about category or style, vad är det för musik is the normal choice.

Because musik is being used in a general, uncountable sense.

You are asking about a category:

• what kind of music

not about some specific music already known to both speakers:

• the music

That is why Swedish uses musik, not musiken.

This is similar to English:

• What kind of music does she listen to? not
• What kind of the music does she listen to?

Because hon lyssnar på is describing musik. It works a bit like a relative clause in English:

• the music [that she listens to]

So the structure is roughly:

• Vad är det för musik = What kind of music
• hon lyssnar på = she listens to
• när hon jobbar = when she works / while she is working

Put together:

• What kind of music she listens to when she works?

But since it is a question, the natural English translation is:

• What kind of music does she listen to when she works?

Because the verb is lyssna på, which means listen to.

In Swedish, when the object is moved or expanded, the preposition often stays later in the clause:

• Hon lyssnar på musik. = She listens to music.
• musiken hon lyssnar på = the music she listens to

This is very similar to natural English:

• the music she listens to

So på belongs with lyssnar, even though it appears later.

It is best to think of it as a verb + fixed preposition combination:

• lyssna på = listen to

You usually need the på when you say what someone is listening to.

Examples:

• Hon lyssnar på radio. = She listens to the radio.
• Jag lyssnar på jazz. = I listen to jazz.

So learners should memorize lyssna på together.

Swedish actually has more than one possible way to ask this kind of question.

Your sentence uses the pattern:

• Vad är det för musik ...?

This is a fixed and very common way to ask what kind of music ...?

Another possible pattern is:

• Vad lyssnar hon på för musik?

That is also possible in Swedish and also means:

• What kind of music does she listen to?

The version in your sentence is especially useful because it focuses very clearly on what kind of.

Here när hon jobbar can often be understood as either:

• when she works
• when she is working
• while she works / while she is working

In this sentence, it most likely means during the times when she is working.

Because Swedish present tense is often broader than English present tense, jobbar can correspond to:

• works
• is working

depending on context.

Both are possible, but jobbar is more common in everyday spoken Swedish.

• jobbar = more everyday, conversational
• arbetar = more formal or neutral-written

So:

• när hon jobbar sounds natural and everyday.

If you said:

• när hon arbetar

that would still be correct, just a bit more formal in tone.

By default, it sounds like a habitual question:

• What kind of music does she listen to when she works?

That is, in general, during work.

The Swedish present tense often covers habitual actions very naturally:

• hon lyssnar
• hon jobbar

If you wanted to make it clearly about one specific moment, the context would usually have to show that.

Yes, very often. It is a very useful pattern.

Examples:

• Vad är det för film? = What kind of film is it?
• Vad är det för mat? = What kind of food is it?
• Vad är det för problem? = What kind of problem is it?

So in your sentence:

• Vad är det för musik ...?

the same pattern is being used with musik.

A helpful way to break it down is:

• Vad är det för musik = What kind of music
• hon lyssnar på = she listens to
• när hon jobbar = when she works

So the sentence structure is basically:

What kind of music + she listens to + when she works

Even though English needs does she listen to in a direct question, Swedish does not build it the same way here because of the idiomatic vad är det för pattern.