A barátom szeretné, ha az ünnepelt elfújná a tortagyertyát.

Because Hungarian usually does not use an infinitive when the subject of the main verb and the subject of the second action are different.

In English, you can say:

• My friend would like the celebrant to blow out the candle.

In Hungarian, that idea is normally expressed as:

• szeretné, ha az ünnepelt elfújná...
• literally something like would like it if the celebrant blew out...

If the same person does both actions, Hungarian can use an infinitive more easily. But here my friend and the celebrant are different people, so szeretné, ha... is the natural pattern.

Szeretné is the conditional form of szereti? Not exactly in meaning. Here it comes from szeretne / szeretné, which means would like.

So:

• szeret = likes / loves
• szeretne = would like
• szeretné = would like it / would like that

In this sentence, A barátom szeretné... means My friend would like...

The ending -né is the conditional definite form, which fits because what follows is treated as a definite content: ha az ünnepelt elfújná a tortagyertyát.

In the pattern szeretné, ha..., the verb in the ha clause is very often in the conditional too.

So Hungarian says:

• szeretné, ha az ünnepelt elfújná...

This is the normal way to express would like someone to do something.

Even though ha often means if, in this construction the whole phrase is more idiomatic and does not sound like a real condition in English. It is just how Hungarian builds this idea.

Formally, yes: ha normally means if.

But in this sentence, ha is part of the fixed pattern:

• szeretné, ha...

This often corresponds to English:

• would like someone to...
• would like it if...
• sometimes wants ... to... depending on context

So you should not translate it too literally word for word. Here it is best understood as part of the whole structure, not as a separate logical if.

Because the verb has a definite object:

• a tortagyertyát = the cake candle

Hungarian verbs often have two kinds of conjugation:

• indefinite
• definite

Since the object is definite, Hungarian uses the definite conditional form:

• elfújna = indefinite
• elfújná = definite

So elfújná a tortagyertyát is correct because the action is being done to a specific object.

El- is a verbal prefix. With fúj (to blow), it creates the meaning blow out or blow away/completely depending on context.

Here:

• fúj = blow
• elfúj = blow out

So:

• elfújná a tortagyertyát = would blow out the cake candle

Without el-, the meaning would be much less specific.

Yes, Hungarian verbal prefixes often move, but only in certain situations.

In a neutral clause, the prefix usually stays attached:

• az ünnepelt elfújná a tortagyertyát

But if something is strongly focused, negated, or in some other special structures, the prefix can move:

• Az ünnepelt fújná el a tortagyertyát.
  This could put stronger focus on the celebrant.

So in your sentence, the attached form elfújná is the normal neutral order.

Ünnepelt literally means the celebrated one or the person being celebrated.

It comes from the verb ünnepel = to celebrate.
As a form, ünnepelt is a participle, but in real usage it often works like a noun:

• az ünnepelt = the celebrant / the person whose special day it is

In a birthday context, it can mean something like:

• the birthday person
• the guest of honor

Because Hungarian usually marks possession with an ending on the noun itself.

• barát = friend
• barátom = my friend

The ending -om shows my.

Hungarian can still use the article before a possessed noun:

• A barátom = My friend

That article is normal in Hungarian, even though English usually leaves it out.

Hungarian often uses the definite article before possessed nouns when they are the subject or otherwise definite in the sentence.

So:

• A barátom szeretné...

is perfectly normal Hungarian.

English says:

• My friend would like...

without the, but Hungarian grammar works differently here. The article does not make it sound unnatural or overly specific; it is just standard Hungarian usage.

Tortagyertyát has two important parts:

1. tortagyertya = cake candle

   • torta = cake
   • gyertya = candle

2. -t = accusative ending
   This marks the direct object of the verb.

So:

• a tortagyertyát = the cake candle as the object of elfújná

You may also notice the final vowel lengthens:

• tortagyertya → tortagyertyát

That is a normal spelling/pronunciation pattern in Hungarian when certain endings are added.

The sentence simply uses the singular noun:

• a tortagyertyát = the cake candle

That may refer to one candle, or it may just be the specific phrasing chosen in this example.

If you wanted candles, Hungarian would use the plural:

• a tortagyertyákat

So this is not a special grammar rule here; it is just singular because the sentence says singular.

The word order is fairly natural and neutral as given:

• A barátom szeretné, ha az ünnepelt elfújná a tortagyertyát.

But Hungarian word order is flexible, and changing it often changes the emphasis.

For example, if you want to emphasize the celebrant, you might get a different structure or stress pattern. If you want a neutral statement, the original order is a good model.

So the answer is:

• the sentence is natural as written
• other orders are possible
• but different orders usually add emphasis or contrast rather than just sounding stylistically different

Grammatically, you could build a similar sentence with akarja (wants), but the meaning and tone would change.

• szeretné = would like
  softer, more polite, less forceful
• akarja = wants
  stronger, more direct

So:

• A barátom szeretné, ha... = My friend would like...
• A barátom akarja, hogy... or another structure with akar would sound more like My friend wants...

In this sentence, szeretné sounds more natural if the intention is polite or gentle.