Huic puellae duo fratres sunt, sed illi puero nulla soror est.

Because Latin is using the dative of possession.

Instead of saying the girl has two brothers, Latin often says something more like:

• To this girl, there are two brothers
• To that boy, there is no sister

So:

• huic puellae = for/to this girl
• illi puero = for/to that boy

The actual grammatical subjects are:

• duo fratres
• nulla soror

Those are the things that are.

Latin often expresses possession in two different ways:

• with habere = to have
• with the dative + esse = literally to someone there is ...

In this sentence, Latin chooses the second pattern:

• Huic puellae duo fratres sunt
• literally: To this girl, two brothers are

This is a very common and important construction in Latin, especially in simple statements of possession.

Here puellae is dative singular.

That may look confusing at first, because puellae can also be:

• genitive singular
• dative singular
• nominative plural
• vocative plural

But in this sentence, huic makes the function clear. Since huic is dative singular, puellae is also dative singular:

• huic puellae = to/for this girl

Because the demonstratives have to match the noun they go with.

• huic matches puellae
• illi matches puero

Both are dative singular, but:

• huic can be used for masculine, feminine, or neuter in the dative singular
• illi is also dative singular and likewise agrees with its noun in case, number, and gender

So:

• huic puellae = to this girl
• illi puero = to that boy

The difference is in the demonstrative idea:

• hic, haec, hoc = this
• ille, illa, illud = that

Because duo fratres is the subject, so it must be in the nominative case.

• duo = nominative masculine plural
• fratres = nominative masculine plural

If it were a direct object, you would expect the accusative:

• duos fratres

But here the brothers are not being acted on. They are the things that exist / are possessed, so they are nominative.

For the same reason: nulla soror is the subject of est.

• nulla = nominative feminine singular
• soror = nominative feminine singular

So Latin is literally saying:

• No sister exists for that boy

If it were a direct object, then you would see accusative forms such as nullam sororem.

Latin often uses the singular to mean not even one.

So nulla soror est means:

• there is no sister
• in natural English: he has no sister

If you wanted to say no sisters more explicitly as a plural idea, Latin could also use:

• nullae sorores

But the singular is perfectly natural when the point is not even one sister.

Because the verb agrees with the subject.

In the first clause, the subject is plural:

• duo fratres = two brothers
• so Latin uses sunt = are

In the second clause, the subject is singular:

• nulla soror = no sister
• so Latin uses est = is

So the verb agrees with what exists, not with the possessor.

Yes, but not because Latin word order is fixed the way English word order is.

Latin word order is much freer because the case endings show the grammatical relationships. In this sentence, the order helps emphasize contrast:

• Huic puellae ... = to this girl
• sed illi puero ... = but to that boy

Putting those phrases early makes the contrast very clear.

A Latin speaker could rearrange the words and still keep the same basic meaning, as long as the case endings stayed the same. But this order is neat and natural.

A useful rule is this:

With dative of possession + esse,

• the possessor is in the dative
• the thing possessed is in the nominative

So here:

• huic puellae = possessor
• duo fratres = thing possessed

and:

• illi puero = possessor
• nulla soror = thing possessed

That is why fratres and soror are nominative.

Because Classical Latin has no articles like English a/an/the.

So a noun like puella can mean:

• girl
• a girl
• the girl

depending on context.

The same is true here:

• duo fratres can be understood as two brothers
• nulla soror as no sister

English has to choose an article or determiner; Latin usually does not.

The big pattern is:

dative possessor + nominative thing possessed + esse

So you can think:

• mihi liber est = I have a book
  literally, to me a book is

And in this sentence:

• huic puellae duo fratres sunt
• illi puero nulla soror est

If you remember that pattern, this sentence becomes much easier to read.