imouto ha maturi ni kite iku yukata wo kinou erabimasita.

A helpful way to break it up is:

• 妹は = as for my younger sister
• 祭りに着て行く浴衣を = the yukata that she will wear to the festival
• 昨日 = yesterday
• 選びました = chose

So the whole sentence is structured like:

• [Topic] 妹は
• [Object] 祭りに着て行く浴衣を
• [Time] 昨日
• [Verb] 選びました

Japanese often puts a long descriptive phrase before the noun it modifies, so 祭りに着て行く comes before 浴衣.

In Japanese, words like 妹 often do not need an explicit my when the relationship is obvious from context.

So:

• 妹 = younger sister
• in many normal contexts, it naturally means my younger sister

If you needed to be more explicit, you could say:

• 私の妹 = my younger sister

But in everyday Japanese, 私の is often omitted when it is already clear.

This is a noun-modifying clause.

Break it down like this:

• 祭りに = to the festival
• 着て行く = wear and go
• 浴衣 = yukata

So literally, it is:

• the yukata [she will wear and go to the festival in]

In natural English, we usually say:

• the yukata she will wear to the festival

Japanese does not need a word like that or which here. The clause just comes directly before the noun:

• 祭りに着て行く浴衣 = the yukata that she will wear to the festival

Here, に marks the destination of 行く.

• 祭りに行く = go to the festival

Since 着て行く includes 行く, the に still belongs with that idea of going:

• 祭りに着て行く = wear it and go to the festival / wear it to the festival

You may also see へ with destinations, but に is very common and natural here.

着て行く literally means put on/wear and go.

So:

• 着る = to wear / put on
• 着て行く = to wear and go somewhere

In this sentence, it suggests the yukata is the clothing she will have on when she goes to the festival. In English, we usually simplify that to:

• wear to the festival

So 着て行く is a very natural Japanese way to express wear something to an event/place.

Because 昨日 modifies the main verb 選びました:

• 昨日選びました = chose yesterday

Japanese time expressions are often placed before the verb they modify. The position is fairly flexible, but this order is very natural.

Also, placing 昨日 here helps show that it is the choosing that happened yesterday, not the wearing.

So the meaning is:

• She chose it yesterday
• not: she will wear it yesterday (which would not make sense)

は marks the topic, while が more strongly marks the subject or gives it focus.

With 妹は, the sentence feels like:

• As for my younger sister, she chose...

This is a very natural way to talk about someone as the topic of the sentence.

If you said 妹が, it would sound more like you are emphasizing that it was my younger sister who chose it, perhaps in contrast with someone else.

So:

• 妹は = neutral topic-setting
• 妹が = stronger focus on younger sister

Because 浴衣 is the direct object of 選びました.

• 浴衣を選びました = chose a yukata

Even though 浴衣 has a long modifier before it:

• 祭りに着て行く浴衣

the whole noun phrase still functions as the object, so を comes after the noun:

• 祭りに着て行く浴衣を選びました
• chose the yukata she will wear to the festival

Yes. 選びました is the polite past form of 選ぶ.

• dictionary form: 選ぶ = to choose
• plain past: 選んだ = chose
• polite past: 選びました = chose

So the sentence is written in polite style. A plain-style version would be:

• 妹は祭りに着て行く浴衣を昨日選んだ。

No, not in ordinary Japanese writing. The sentence would normally be written as:

• 妹は祭りに着て行く浴衣を昨日選びました。

The spaces in your example are just there to make it easier for learners to see the parts of the sentence. In real Japanese text, words are usually written without spaces.