Mojoj sestri se danas pije limunada, a meni se jede nešto slatko iz slastičarnice.

Because Croatian is using the dative case for the person who experiences the craving.

The pattern is:

[person in dative] + se + verb

So:

• moja sestra = my sister (nominative, dictionary form)
• mojoj sestri = to my sister / my sister in this construction
• ja = I
• meni = to me / me in this construction

This dative-for-experiencer pattern is very common in Croatian:

• Meni se spava. = I feel sleepy / I feel like sleeping.
• Njemu se ne radi. = He doesn’t feel like working.
• Djeci se igra. = The children feel like playing.

Also, mojoj agrees with sestri: both are feminine singular dative.

Here se is part of a very common Croatian idiom. It does not literally mean oneself in the English sense.

With verbs like jesti, piti, spavati, raditi, Croatian often uses:

jede mi se, pije mi se, spava mi se, radi mi se

This expresses a current urge, craving, or inclination:

• jede mi se = I feel like eating
• pije mi se = I feel like drinking
• spava mi se = I feel like sleeping

So in this sentence, se helps form that special feel-like construction. It is best learned as a whole pattern, not translated word-for-word.

Because mojoj sestri and meni are not the grammatical subjects here.

In English, we say my sister wants... or I feel like eating..., so the person seems to be the subject. But in Croatian, in this construction, the person is in the dative, and the verb is not conjugated to match that person.

So Croatian says, literally in structure:

• To my sister, lemonade is drinkable / drink-desirable today
• To me, something sweet is eat-desirable

That sounds strange in English, but it explains why the verb is not pijem/jedem.

In this sentence, the verbs appear in singular form because the desired things are singular ideas:

• limunada = singular
• nešto slatko = singular idea

Normally, yes:

• Pijem limunadu. = I am drinking lemonade.

There, limunadu is accusative because piti is a normal transitive verb.

But in the special craving construction pije mi se..., Croatian often uses the thing wanted in the nominative:

• Pije mi se kava.
• Pije mi se limunada.

So limunada is expected here.

This is one of those places where Croatian does not follow the ordinary verb-object pattern that an English speaker may expect. It is a very common and natural colloquial structure.

Because nešto behaves like a neuter singular word in this type of phrase, so the adjective also appears in neuter singular:

• nešto lijepo = something nice
• nešto novo = something new
• nešto slatko = something sweet

So slatko agrees with nešto.

This is very common in Croatian and other Slavic languages: after words like nešto, the adjective is usually neuter singular.

Iz slastičarnice means from the pastry shop / confectionery / dessert shop.

The preposition iz requires the genitive case, so:

• slastičarnica = nominative
• iz slastičarnice = genitive after iz

Other examples:

• iz škole = from school
• iz grada = from the city
• iz pekarnice = from the bakery

So the form slastičarnice is there because iz always triggers genitive.

A slastičarnica is a place associated with sweets and desserts: cakes, pastries, ice cream, and similar items.

A pekarnica is a bakery, mainly associated with bread, baked goods, burek, savory pastries, and everyday bakery items.

So nešto slatko iz slastičarnice suggests something specifically sweet from a dessert/pastry shop, not just any baked item.

Because a often connects two related statements with a mild contrast.

Here the idea is:

• My sister feels like lemonade today,
• whereas I feel like something sweet...

So a works well because the two people want different things.

Compare:

• i = and, simple addition
• a = and / while / whereas, often with contrast

In this sentence, a is the more natural choice.

Croatian word order is flexible, but clitics like se tend to go in second position in the clause.

That is why:

• Mojoj sestri se danas pije limunada sounds natural.

Here, Mojoj sestri is the first phrase, and se comes right after it.

You could also rearrange the sentence for emphasis, for example:

• Danas se mojoj sestri pije limunada.

That is also possible, because now Danas is first, and se still stays in second position.

So the word order is not random; it follows a common clitic-placement rule.

Because meni is the full, stressed form of the dative pronoun, while mi is the unstressed clitic form.

In this sentence, a meni creates a natural contrast:

• my sister ... but as for me ...

So meni is used for emphasis and contrast.

Compare:

• Meni se jede nešto slatko. = As for me, I feel like eating something sweet.
• Jede mi se nešto slatko. = I feel like eating something sweet.

Both are correct, but meni is stronger and more contrastive.

Yes, you could, but the nuance would change.

• želi piti / želi jesti = wants to drink / wants to eat
• pije se / jede se with dative = feels like drinking / feels like eating

The sentence you were given sounds more natural for a current craving or appetite.

So:

• Mojoj sestri se danas pije limunada...
  feels like My sister is in the mood for lemonade today

while

• Moja sestra želi piti limunadu...
  sounds more direct and deliberate: My sister wants to drink lemonade

Croatian often prefers the dative + se pattern when talking about cravings, appetite, or mood.