Learn Hardcore Croatian: Naslov članka je kratak, ali priča o siromašnoj djevojci je duga. - The title of the article is short, but the story about the poor girl is long.

Članak is the basic (dictionary) form, nominative singular.
In the phrase naslov članka (the title of the article), članka is in the genitive singular.

Croatian often uses the second noun in the genitive to show possession or a close relationship, similar to "of" in English:

naslov članka = title of the article
boja auta = color of the car (from auto)
vrh planine = top of the mountain (from planina)

So članka = of the article.

What case is siromašnoj djevojci, and why is it used here?

Siromašnoj djevojci is in the locative singular feminine.

The preposition o (meaning about, of in the sense of concerning) in Croatian always takes the locative case:

priča o siromašnoj djevojci = a story about a poor girl
govoriti o problemu = to talk about the problem
razmišljam o tebi = I’m thinking about you

So:

djevojka (nominative) → djevojci (locative)
siromašna (nominative fem. sg.) → siromašnoj (locative fem. sg., agreeing with djevojci)

Why is it kratak but duga? Why don’t both adjectives have the same ending?

The form of the adjective depends on the gender of the noun it describes:

naslov is masculine, so we use kratak (masculine nominative singular).
priča is feminine, so we use duga (feminine nominative singular of dug).

So we have:

naslov (m.) je kratak – the title is short
priča (f.) je duga – the story is long

Adjectives in Croatian must agree in gender, number, and case with the noun they modify.

Why is the verb je repeated? Could we say it only once?

In the sentence:

Naslov članka je kratak, ali priča o siromašnoj djevojci je duga.

the verb je (is) appears in both clauses.

Grammatically, in Croatian you can drop the second je in casual speech:

Naslov članka je kratak, ali priča o siromašnoj djevojci duga.

However:

Keeping je in both parts is clearer and more natural in standard written language.
Omitting it in the second clause sounds more colloquial and a bit more literary/stylistic.

So the original version (with two je) is perfectly standard and often preferred, especially in writing.

Why is the comma placed before ali?

Ali means but and introduces a contrast.
In Croatian, a comma is normally required before ali when it connects two clauses:

Volim ga, ali mu ne vjerujem. – I like him, but I don’t trust him.
Bilo je hladno, ali sunčano. – It was cold, but sunny.

So:

Naslov članka je kratak, ali priča o siromašnoj djevojci je duga.

has a comma before ali because it connects two clauses that contrast with each other.

Why is the word order Naslov članka je kratak and not Je naslov članka kratak?

In statements, Croatian usually starts with the subject or another content word, and puts the short verb form je (a clitic) in the second position in the clause:

Naslov članka je kratak. – subject (Naslov članka) + je
- predicate (kratak)

Je almost never goes first in a statement.
Je naslov članka kratak? looks like a question, not a statement.

Compare:

Statement: Naslov članka je kratak. – The title of the article is short.
Question: Je li naslov članka kratak? – Is the title of the article short?

What is the difference between priča o siromašnoj djevojci and siromašna djevojka?

siromašna djevojka = a poor girl (the girl herself is the subject or object of the sentence)
- Siromašna djevojka čita. – The poor girl is reading.
priča o siromašnoj djevojci = a story about a poor girl
Here, priča (the story) is the main noun, and o siromašnoj djevojci just says what the story is about.

So in:

... ali priča o siromašnoj djevojci je duga.

the focus is on the story, not directly on the girl.

Can the word order change to Duga je priča o siromašnoj djevojci? Does that sound natural?

Yes, Croatian allows flexible word order, and:

Duga je priča o siromašnoj djevojci.

is grammatically correct and natural.
However, changing the word order slightly changes the emphasis:

Priča o siromašnoj djevojci je duga. – neutral; just a statement of fact.
Duga je priča o siromašnoj djevojci. – puts more emphasis on duga (long), a bit more stylistic or expressive.

In your original sentence, the more neutral order is used.

Why is it duga and not dugo?

Duga is the feminine nominative singular adjective, matching priča (feminine noun).

Dugo can be:

neuter form of the adjective dug (long), or
an adverb meaning for a long time.

Here we need an adjective describing a feminine noun (priča), so:

priča je duga – the story is long (feminine)
putovanje je dugo – the trip is long (neuter)
Dugo čekam. – I’ve been waiting for a long time. (adverb)

How do the adjective endings in siromašnoj djevojci work?

Siromašnoj is the adjective siromašan (poor) in the feminine, singular, locative form, agreeing with djevojci.

Pattern (feminine singular of siromašan):

Nominative: siromašna – a poor girl (siromašna djevojka)
Genitive: siromašne
Dative: siromašnoj
Accusative: siromašnu
Locative: siromašnoj
Instrumental: siromašnom

Since o requires locative, we use siromašnoj djevojci, not siromašna djevojka.