Для торта мы купили длинные свечи, а для детей — яркие шарики.

Because для requires the genitive case.

So:

• торт → для торта
• дети → для детей

This is a very common pattern in Russian:

• для мамы = for mom
• для друга = for a friend
• для детей = for children

So in this sentence, для торта and для детей both mean for the cake and for the children, with the nouns in the genitive.

They actually are in the accusative, but for inanimate plural nouns, the accusative usually looks the same as the nominative.

So:

• свечи can be nominative plural or accusative plural
• шарики can be nominative plural or accusative plural

Here they are the direct objects of купили, so they are in the accusative plural:

• купили свечи
• купили шарики

This is normal in Russian. Compare:

• Я вижу столы = I see tables
• столы is accusative plural, but it looks just like nominative plural

The adjectives must agree with the nouns they describe in number, gender, and case.

Here both nouns are:

• plural
• accusative
• inanimate

So the adjectives also take the plural form:

• длинные свечи
• яркие шарики

Because these are inanimate plural objects, the accusative plural matches the nominative plural, so the adjective forms are the same ones you would also see in the nominative plural.

А often connects two ideas with a sense of contrast, pairing, or comparison, even when English would simply use and.

Here the sentence is dividing the purchases into two groups:

• for the cake → long candles
• for the children → bright balloons

So а works well because it sets up a contrast or distribution: one thing for this, another thing for that.

If you used и, it would sound more like a simple list.
With а, the sentence feels more like:

• for the cake, we bought long candles, whereas / and for the children, bright balloons

The dash shows that something has been left out because it is understood from the first part of the sentence.

The full version would be:

• Для торта мы купили длинные свечи, а для детей мы купили яркие шарики.

Russian often avoids repeating words that are obvious from context. So after а для детей, the verb купили is omitted, and the dash marks that omission.

This is very natural Russian style.

Yes, but the meaning and style would shift a little.

Possible full version:

• Для торта мы купили длинные свечи, а для детей купили яркие шарики.

Possible version with the subject repeated too:

• Для торта мы купили длинные свечи, а для детей мы купили яркие шарики.

The dash version is more compact and elegant:

• Для торта мы купили длинные свечи, а для детей — яркие шарики.

So the dash is not random punctuation; it helps show that the verb is omitted on purpose.

Yes, Russian could leave it out:

• Для торта купили длинные свечи, а для детей — яркие шарики.

Russian often omits subject pronouns when they are clear from the verb ending.
But мы is included here because it sounds natural and can make the sentence a bit clearer or more grounded:

• we bought long candles...
• and for the children, bright balloons

So мы is not strictly necessary, but it is perfectly normal.

Russian word order is flexible, and moving Для торта to the front gives it emphasis.

The sentence is organized by purpose/recipient first:

• for the cake → long candles
• for the children → bright balloons

That structure makes the contrast very clear.

A more neutral word order is also possible:

• Мы купили длинные свечи для торта, а яркие шарики — для детей.

But the original version highlights the two for... phrases more strongly.

Both words relate to balls/balloons, but шарики is very common when talking about party balloons.

• шар = ball / sphere / balloon
• шарик = little ball / balloon

In everyday Russian, especially in festive contexts, шарики often sounds more natural and friendly than шары.

So in a birthday-party type sentence, яркие шарики is exactly what many native speakers would expect.

Yes, literally it is for the cake. Russian is focusing on the intended use of the candles, not their physical position.

So для торта means:

• intended for the cake
• meant to go with the cake
• to be used for the cake

In context, that naturally means birthday candles for putting on a cake.

Russian often uses для this way to show purpose:

• ложка для супа = a spoon for soup
• подарок для друга = a gift for a friend
• свечи для торта = candles for a cake

Because а is joining two coordinated parts of the sentence, and in Russian that normally requires a comma.

So the structure is:

• first clause: Для торта мы купили длинные свечи
• second clause: а для детей — яркие шарики

The comma separates these two linked parts, just as you would often separate clauses in English.

So the punctuation pattern here is standard:

• ..., а ...