Ana i Sara jedna drugoj pišu kratka pisma.

It is the reciprocal expression meaning to each other or to one another.

Because the two people are female, Croatian uses feminine forms:

• jedna
• drugoj

So Ana i Sara jedna drugoj pišu kratka pisma means that Ana writes to Sara and Sara writes to Ana.

That is normal in this Croatian reciprocal pattern. Even though Ana i Sara is plural, Croatian often expresses reciprocity with singular forms built from jedan and drugi.

So the phrase is singular in form, but its meaning is plural and mutual: each to the other.

In this construction, the first part normally stays in the nominative, while the second part shows the case required by the sentence.

Here:

• jedna = nominative feminine singular
• drugoj = dative feminine singular

So jedna drugoj is the expected form.

Because pisati uses the dative for the person you write to.

A very common pattern is:

• pisati komu? = to write to whom?
• pisati što? = to write what?

So in this sentence:

• jedna drugoj = the person each one writes to
• kratka pisma = what they write

Because jedna drugu would be used when each other is a direct object, not an indirect object.

For example:

• Ana i Sara vide jedna drugu = Ana and Sara see each other

But with pisati, the other person is the recipient, so Croatian uses the dative:

• Ana i Sara pišu jedna drugoj

Because the subject is Ana i Sara, which is plural.

So the verb must be in the 3rd person plural:

• piše = he/she writes
• pišu = they write

Because pismo is a neuter noun, and here it is plural.

So:

• pismo = letter
• pisma = letters

The adjective must agree with the noun:

• kratka = neuter plural
• pisma = neuter plural

Together, kratka pisma means short letters.

It is accusative plural, because it is the direct object of pišu.

However, with many neuter inanimate nouns in Croatian, the nominative and accusative plural look the same. So pisma could be nominative plural in another sentence, but here it is accusative plural because it is the thing being written.

No. Croatian word order is fairly flexible.

The original sentence is natural and neutral:

• Ana i Sara jedna drugoj pišu kratka pisma

But you could also say:

• Ana i Sara pišu kratka pisma jedna drugoj

Both are grammatical. The difference is mostly about emphasis and style, not basic meaning.

It can mean either, depending on context.

The verb pisati is imperfective, and the Croatian present tense can express:

• a habitual action: Ana and Sara write short letters to each other
• an action happening now: Ana and Sara are writing short letters to each other

Context tells you which meaning is intended.

Because Croatian does not have articles.

So kratka pisma can mean:

• short letters
• the short letters
• sometimes some short letters

English must choose an article, but Croatian usually leaves that information to context.

Yes. That is also a very natural Croatian sentence.

Here, si is a dative clitic, and si pišu often means write to each other.

So both of these are natural:

• Ana i Sara si pišu kratka pisma
• Ana i Sara jedna drugoj pišu kratka pisma

If you already use jedna drugoj, adding si is usually unnecessary, because the reciprocal meaning is already clear.