Hennes humör blir bättre när alla visar respekt och lyssnar på vad hon säger.

Because a possessive like hennes already makes the noun definite. In Swedish, you normally do not add the definite ending when you use min, din, hans, hennes, vår, etc.

So:

• humör = mood
• hennes humör = her mood

Not hennes humöret.

Swedish uses sin/sitt/sina only when the possessor is the subject of the same clause.

Here, the possessor is hon understood from hennes, but the subject of the main clause is humör, and in the subordinate clause the subject is alla. So sin does not fit.

That is why hennes is correct.

A quick comparison:

• Hon lyssnar på sin lärare. = She listens to her own teacher.
• Alla lyssnar på hennes lärare. = Everyone listens to her teacher.

Blir is from bli, which means become / get. It shows a change.

So humöret blir bättre means her mood gets better or becomes better.

If you used är bättre, that would describe a state instead of a change:

• Hennes humör blir bättre = Her mood gets better.
• Hennes humör är bättre = Her mood is better.

The basic form is bra = good.

Its comparison forms are irregular:

• bra = good
• bättre = better
• bäst = best

So blir bättre means gets better.

Here alla means everyone / everybody.

When alla stands by itself, it often means everyone. When it comes before a noun, it can mean all:

• Alla lyssnar. = Everyone is listening.
• Alla människor lyssnar. = All people are listening.

När means when, while om usually means if.

In this sentence, the idea is that her mood improves when people show respect and listen to her, not if maybe they do.

So:

• när = when
• om = if

In many contexts, när can also mean whenever.

Because respekt is usually treated as an abstract, uncountable noun here. Swedish often uses it without an article in this expression.

Visa respekt is a very common phrase meaning show respect.

So:

• visa respekt = show respect

Using en respekt would sound unnatural here.

Because lyssna normally takes the preposition på when you say what or whom someone is listening to.

So:

• lyssna på någon = listen to someone
• lyssna på något = listen to something

Examples:

• Jag lyssnar på henne. = I listen to her.
• De lyssnar på musik. = They listen to music.

This is just how the verb works in Swedish.

It means what she says.

Here vad introduces the content of what is being listened to. So lyssnar på vad hon säger means listen to what she says.

It is not a question here. It is an embedded clause.

Because this is an embedded clause, not a direct question.

In direct questions, Swedish often has verb-before-subject order:

• Vad säger hon? = What is she saying? / What does she say?

But in embedded clauses, the subject comes before the verb:

• Jag hör vad hon säger. = I hear what she says.
• De lyssnar på vad hon säger. = They listen to what she says.

So vad hon säger is the correct word order here.

Because när alla visar respekt is a subordinate clause, and subordinate clauses in Swedish normally keep subject-before-verb order.

So the normal pattern is:

• när + subject + verb

That gives:

• när alla visar respekt
• när hon kommer
• när vi äter

Verb-before-subject order is used in main clauses in certain situations, but not here.

Because the same subject, alla, applies to both verbs:

• visar
• lyssnar

So Swedish, like English, can leave the subject unstated the second time:

• alla visar respekt och lyssnar på vad hon säger

This means:

• everyone shows respect
• and everyone listens to what she says

You could repeat alla, but it is usually unnecessary here.