Antes de que empiece la segunda película, mi hermana quiere comprar otra copa de vino y yo unas palomitas pequeñas.

Because antes de que is followed by the subjunctive when it introduces an action that has not happened yet.

Here, Antes de que empiece la segunda película means the second film has not started yet at the moment we are talking about, so Spanish uses the subjunctive:

• antes de que + subjunctive
• antes de que empiece

This is very common:

• Antes de que llegues, voy a salir.
• Antes de que termine la clase, haz la pregunta.

So the subjunctive is not there because the speaker doubts it will happen, but because it is a future, pending action after antes de que.

In modern standard Spanish, the normal structure is antes de que + subjunctive.

So you say:

• Antes de que empiece...

not:

• Antes que empiece... in this context

There is also antes de + infinitive when the subject is the same:

• Antes de entrar, compré agua.
  = Before entering, I bought water.

But when there is a full clause with a different verb and subject, Spanish usually uses:

• antes de que + subjunctive

In your sentence, the subject of empiece is la segunda película, so a full clause is needed.

Not in the same way.

Antes de empezar la segunda película would usually mean before starting the second film, with an infinitive. That sounds like someone is going to start it, and it does not match the idea as naturally.

Your sentence means:

• Before the second film starts...

That is why Antes de que empiece la segunda película is the natural choice.

A useful rule:

• Use antes de + infinitive when there is no new subject.
• Use antes de que + subjunctive when there is a new subject or a full clause.

The verb is empezar, and it is a stem-changing verb: e → ie.

In the present subjunctive, it goes:

• yo empiece
• tú empieces
• él/ella empiece
• nosotros empecemos
• vosotros empecéis
• ellos/ellas empiecen

So empiece is the correct present subjunctive form.

Also notice the spelling change:

• empezar has z
• but before e, Spanish changes z to c
• so: empiece, empieces, etc.

This keeps the pronunciation consistent.

Yes, Spanish often drops subject pronouns because the verb ending usually makes the subject clear.

But here yo is included for contrast:

• mi hermana quiere comprar otra copa de vino y yo unas palomitas pequeñas

The idea is:

• my sister wants to buy... and I want...

Spanish includes yo to highlight the contrast between what the sister wants and what the speaker wants.

If you removed yo, the sentence would sound less balanced and less clear.

Because Spanish often omits repeated words when they are easy to understand from the context. This is called ellipsis.

Full version:

• mi hermana quiere comprar otra copa de vino y yo quiero comprar unas palomitas pequeñas

Natural shortened version:

• mi hermana quiere comprar otra copa de vino y yo unas palomitas pequeñas

In English we do something similar:

• My sister wants wine, and I popcorn.

That sounds a bit more limited in English, but in Spanish this kind of omission is very normal when the missing verb is obvious.

If you wanted, you could say the full version:

• ...y yo quiero comprar unas palomitas pequeñas.

That is also correct.

Because otro / otra already includes the idea of another, so you do not normally use un/una before it.

So:

• otra copa = another glass
• not una otra copa

Compare:

• Quiero otra cerveza.
• Necesitamos otro billete.
• Voy a pedir otra ración.

This is the same idea as English another, which also does not usually need an extra article before it.

Because copa de vino specifies the serving/container: a glass of wine.

So:

• vino = wine
• una copa de vino = a glass of wine

This is very natural if the speaker wants to say exactly what their sister is going to buy.

In Spain, copa usually means a stemmed glass, especially for wine or an alcoholic drink. A few related words:

• copa = glass, often for wine/drinks
• vaso = drinking glass/tumbler
• botella de vino = bottle of wine

So otra copa de vino is a very natural phrase.

Because Spanish treats palomitas as a plural countable noun in this common meaning.

In Spain, palomitas is the normal word for popcorn, especially cinema popcorn. Even when English uses singular popcorn, Spanish often uses the plural:

• Quiero unas palomitas.
• Compramos palomitas para la película.

So unas palomitas pequeñas means something like:

• a small popcorn
• some small popcorn
• a small serving of popcorn

This is one of those places where Spanish and English organize the idea differently.

Because in Spanish, adjectives usually come after the noun.

So:

• palomitas pequeñas = small popcorn
• segunda película = second film

This is the normal order in most cases.

If an adjective comes before the noun in Spanish, it often changes the tone or emphasis, but here the standard order is best:

• unas palomitas pequeñas

That sounds natural and neutral.

Because the adjective must agree with the noun in gender and number.

Here:

• palomitas is feminine plural
• so the adjective must also be feminine plural

That gives:

• palomitas pequeñas

Agreement pattern:

• palomita pequeña = one small popcorn piece / one small popcorn item
• palomitas pequeñas = small popcorn / small popcorns

Even though in English popcorn does not usually behave this way, in Spanish the adjective still agrees normally with palomitas.

Because ordinal numbers like primero, segundo, tercero usually go with the definite article when you are referring to a specific item in a sequence.

So:

• la segunda película = the second film
• el primer día = the first day
• la tercera vez = the third time

Without the article, it would sound incomplete in this sentence.

Also notice that segunda agrees with película, which is feminine singular:

• la segunda película
• not el segundo película

Yes, but it is not exactly the same nuance.

• otra copa de vino = another glass of wine
• una copa más de vino = one more glass of wine

In many situations they mean almost the same thing. Otra copa is usually the most direct and idiomatic choice here.

So your sentence sounds very natural as it is.

Yes, overall it sounds very Spain-friendly.

A few details:

• película is standard everywhere.
• copa de vino is very normal.
• palomitas is the usual word for popcorn in Spain.

In many parts of Latin America, other words for popcorn are common, such as:

• pochoclo
• crispetas
• palomitas de maíz
• popcorn in some places

So palomitas is a good clue that this sentence fits Spain very well.

Yes. The omitted parts can be restored like this:

• Antes de que empiece la segunda película, mi hermana quiere comprar otra copa de vino y yo quiero comprar unas palomitas pequeñas.

This is grammatically complete and very clear.

The original version is shorter and more natural in everyday speech because Spanish often avoids repeating verbs when the meaning is obvious.