Na tom dortu budou tři svíčky, protože babička chce malou oslavu doma.

Because na means on here, and when na describes a location, Czech uses the locative case.

• na tom dortu = on that/the cake
• na ten dort would normally suggest movement onto the cake, not location

So:

• Je to na tom dortu. = It is on the cake.
• Dám to na ten dort. = I will put it onto the cake.

Czech has no articles, so it does not have a direct equivalent of the or a.

The word ten / ta / to usually means that, but in real sentences it can also help point to a specific known thing, and English may translate it simply as the.

So na tom dortu can feel like:

• on that cake
• or more naturally in context, on the cake

Both are possible depending on the situation.

They change because Czech uses cases.

After na in the meaning of on for location, the noun phrase must be in the locative:

• ten dort = that cake
• na tom dortu = on that cake

So both words change form:

• ten → tom
• dort → dortu

This is very normal in Czech: adjectives, pronouns, and nouns often all change together.

Budou is the 3rd person plural future of být = to be.

Here it means will be.

Because the subject is plural — tři svíčky = three candles — Czech uses plural budou:

• bude = will be, for singular
• budou = will be, for plural

So:

• Na dortu bude svíčka. = There will be one candle on the cake.
• Na dortu budou tři svíčky. = There will be three candles on the cake.

English often uses a dummy subject: there is, there are, there will be.

Czech usually does not need that. It can simply say:

• Na tom dortu budou tři svíčky.
• literally: On that cake will be three candles.

That sounds normal in Czech. The idea of existence is understood from být = to be and the sentence structure.

Because after the numerals two, three, four, Czech normally uses the noun in the plural form.

• jedna svíčka = one candle
• dvě svíčky = two candles
• tři svíčky = three candles
• čtyři svíčky = four candles

But with five and above, Czech usually switches to the genitive plural:

• pět svíček = five candles

So tři svíčky is exactly the form you expect after tři.

Because protože means because and introduces a subordinate clause.

In standard Czech spelling, a subordinate clause introduced by words like protože is separated by a comma:

• Na tom dortu budou tři svíčky, protože babička chce malou oslavu doma.

This is more automatic in Czech than in English. Even when English might feel less strict about punctuation, Czech normally requires the comma.

Because chce = wants takes a direct object, and that object must be in the accusative case.

Base form:

• malá oslava = a small celebration

Accusative form:

• malou oslavu = a small celebration, as the thing being wanted

Both words change because the adjective must agree with the noun:

• malá → malou
• oslava → oslavu

So:

• Babička chce malou oslavu. = Grandma wants a small celebration.

Doma is an adverb meaning at home or home in the sense of one’s home environment.

Czech often uses this adverb without a preposition:

• Jsem doma. = I am at home.
• Chce oslavu doma. = She wants the celebration at home.

This is different from v domě, which means in the house/building and focuses more on the physical building.

So here doma is the natural word because the meaning is at home, not specifically inside a house.

Yes. Czech word order is fairly flexible because the cases show what each word is doing.

The original sentence is natural:

• Na tom dortu budou tři svíčky, protože babička chce malou oslavu doma.

But other orders are possible, with different emphasis:

• Protože babička chce malou oslavu doma, na tom dortu budou tři svíčky.
  This puts the reason first.

• Tři svíčky budou na tom dortu, protože babička chce malou oslavu doma.
  This emphasizes three candles more.

So the meaning stays similar, but the focus changes.

Yes:

• na tom dortu — locative after na
  meaning: on that/the cake

• tři svíčky — nominative plural
  this is the subject: three candles

• babička — nominative singular
  subject of the second clause: grandma

• malou oslavu — accusative singular
  direct object of chce: a small celebration

• doma — adverb
  meaning: at home

So the grammar of the sentence is built mainly from:

• a location phrase,
• a future verb,
• a plural subject,
• and then a because clause with its own subject and object.