Моя сестра мечтает когда-нибудь спеть соло с оркестром.

Because сестра is a feminine noun, and мой (my) has to agree with the noun in gender, number, and case.

• мой брат = my brother
• моя сестра = my sister
• моё письмо = my letter
• мои друзья = my friends

So with сестра, you need моя.

Сестра is in the nominative case because it is the subject of the sentence — the person doing the action.

• Моя сестра = my sister
• мечтает = dreams

So the sentence starts with the subject: My sister dreams...

Мечтать is the dictionary form, the infinitive: to dream.

In the sentence, you need a finite verb: she dreams / she is dreaming.
Since the subject is моя сестра (she), the verb becomes:

• я мечтаю = I dream
• ты мечтаешь = you dream
• он/она мечтает = he/she dreams

So мечтает means dreams.

Когда-нибудь means sometime, one day, or at some point in the future.

In this sentence, it gives the idea that she hopes to do it in the future, but not at any specific time:

• Моя сестра мечтает когда-нибудь спеть...
• My sister dreams of singing ... someday

It often suggests an indefinite future time.

Because когда-нибудь here is just an adverb, not a separate clause.

Russian uses commas mainly to separate clauses or certain inserted expressions. In this sentence, когда-нибудь simply modifies спеть/мечтает, so no comma is needed:

• Она мечтает когда-нибудь спеть. = She dreams of singing someday.

If it were a full clause with когда meaning when, punctuation rules would be different.

This is an aspect question.

• петь = to sing (imperfective)
• спеть = to sing / to sing through / to perform once successfully (perfective)

After мечтать, Russian often uses the infinitive of the action being hoped for. Here, спеть is used because the sentence refers to a single completed performance in the future:

• мечтает спеть соло = dreams of singing a solo

If you said мечтает петь, it would sound more like dreaming of singing in general or being engaged in singing, not one particular performance.

Because in Russian, many verbs can be followed directly by an infinitive to express what someone wants, plans, hopes, or dreams to do.

Examples:

• хочу петь = I want to sing
• люблю читать = I love reading / I love to read
• мечтаю путешествовать = I dream of traveling

So:

• мечтает спеть = dreams of singing / dreams of being able to sing

Russian does not need a word like to before the second verb the way English does.

Yes, соло here is a noun meaning a solo. In Russian, this word is usually treated as an indeclinable noun, meaning it often keeps the same form in different cases.

So you get:

• петь соло = to sing a solo
• слушать соло = to listen to a solo

In this sentence, спеть соло means to sing a solo piece / sing solo.

Because the preposition с meaning with normally requires the instrumental case.

• оркестр = orchestra (nominative)
• с оркестром = with an orchestra (instrumental)

This is a very common pattern:

• с братом = with my brother
• с подругой = with a female friend
• с оркестром = with an orchestra

So the ending -ом shows the instrumental case.

By itself, с оркестром can mean either with an orchestra or with the orchestra, depending on context.

Russian does not have articles like a and the, so you figure that out from the situation. In a general sentence like this, English will usually translate it as with an orchestra.

Yes, Russian word order is fairly flexible, though the neutral order here is very natural:

• Моя сестра мечтает когда-нибудь спеть соло с оркестром.

You could also hear variations like:

• Когда-нибудь моя сестра мечтает спеть соло с оркестром.
• Моя сестра когда-нибудь мечтает спеть соло с оркестром.

But not every change sounds equally natural. The original sentence flows well because it presents:

1. the subject — моя сестра
2. the main idea — мечтает
3. the time nuance — когда-нибудь
4. the dreamed action — спеть соло с оркестром

So the original is a good standard model.

A native speaker would understand it as one idea:

• мечтает = dreams
• когда-нибудь = someday
• спеть = to sing once / to perform

So together:

• мечтает когда-нибудь спеть = dreams of someday singing

The adverb когда-нибудь fits naturally between the main verb and the infinitive, but logically it belongs to the future action.

The stresses are:

• моя́
• сестра́
• мечта́ет
• когда́-нибудь
• спе́ть
• со́ло
• с орке́стром

A rough pronunciation guide:

• моя́ сестра́ мечта́ет когда́-нибудь спе́ть со́ло с орке́стром

Stress is very important in Russian, because it is not always predictable.

Not really. Because of спеть (perfective), the sentence strongly suggests one future performance or the achievement of doing it at least once.

So it sounds like:

• She dreams of someday singing a solo with an orchestra.

If you wanted a more general idea, Russian might use something like петь instead:

• Она мечтает петь с оркестром. = She dreams of singing with an orchestra.

That would sound broader and less like a single special event.