Mi hermana quiere arreglarse para la fiesta.

Because arreglarse is the reflexive form of the verb. In this sentence, it means something like to get oneself ready or to tidy oneself up.

• arreglar = to fix, arrange, tidy
• arreglarse = to get ready, make oneself look nice

So the se shows that the action is being done to herself.

In this context, arreglarse usually means to get ready or to make oneself look nice, especially for a social event.

For example, it can suggest:

• doing her hair
• putting on nice clothes
• doing makeup
• generally getting dressed up

In Spain, arreglarse is a very natural way to talk about getting ready for a party or special occasion.

Because after a conjugated verb like quiere, the second verb stays in the infinitive, and reflexive pronouns can be attached to that infinitive.

So both of these are correct:

• Mi hermana quiere arreglarse para la fiesta.
• Mi hermana se quiere arreglar para la fiesta.

They mean the same thing. Attaching se to the infinitive is very common and sounds natural.

After querer meaning to want, Spanish normally uses infinitive + meaning.

Pattern:

• querer + infinitive

Examples:

• Quiero comer = I want to eat
• Queremos salir = We want to go out
• Mi hermana quiere arreglarse = My sister wants to get ready

So arreglarse stays in the infinitive because quiere is already the conjugated verb.

Yes. That is completely correct.

With a reflexive verb after another conjugated verb, the pronoun can usually go in either place:

• Mi hermana quiere arreglarse para la fiesta
• Mi hermana se quiere arreglar para la fiesta

Both are natural. The first version is often a little neater and is very common in writing.

Because para expresses purpose or intended destination/result here.

She is getting ready for the party in the sense of in preparation for it.

• para = for, in order for, intended for
• por = because of, through, around, by means of, etc.

So:

• arreglarse para la fiesta = to get ready for the party

Using por here would sound unnatural.

Because it refers to a specific party that both speaker and listener can identify.

• la fiesta = the party

Without the article, para fiesta would not be normal here.

Spanish often uses articles where English might also use one, and in this sentence la is the expected choice.

Quiere is the third-person singular present tense of querer.

That means:

• yo quiero = I want
• tú quieres = you want
• él/ella quiere = he/she wants

So Mi hermana quiere... means My sister wants...

Also notice that querer is a stem-changing verb:

• e → ie
• querer → quiere

Because mi here is a possessive adjective meaning my, and that form has no accent.

Compare:

• mi hermana = my sister
• mí = me, myself, after a preposition

Examples:

• Es para mí = It is for me
• Mi hermana = My sister

So in this sentence, mi is correct without an accent.

Often, yes. They overlap, but they are not always identical.

• prepararse = to prepare oneself, get ready
• arreglarse = to get oneself looking nice, tidy oneself up, dress up

For a party, arreglarse often suggests a focus on appearance.
So it can sound a bit more like getting dressed up than prepararse does.

Depending on context, natural English versions could be:

• My sister wants to get ready for the party.
• My sister wants to get herself ready for the party.
• My sister wants to dress up for the party.

The exact choice depends on how much emphasis you want on appearance. Arreglarse often carries that idea of making oneself look nice.

A simple pronunciation guide is:

ah-rreh-GLAR-seh

A few details:

• the rr is a rolled or trilled r
• the stress falls on -glar-
• the final se sounds like seh

In Spain, the s in se is a clear s sound.