Za rođendan smo kupili crveni balon i dugu bijelu vrpcu.

Here za takes the accusative and means something like for a birthday / for the birthday occasion.

So rođendan is in the accusative singular.

Why does it still look like rođendan? Because rođendan is a masculine inanimate noun, and for many masculine inanimate nouns, the accusative singular is identical to the nominative singular.

• nominative: rođendan
• accusative: rođendan

So the form does not change, even though the case does.

Because Croatian often drops subject pronouns when they are not needed.

The sentence already contains smo, which tells you the subject is we:

• sam = I am / I have
• si = you are / you have
• je = he/she/it is / has
• smo = we are / have
• ste = you plural are / have
• su = they are / have

So mi is unnecessary unless you want emphasis:

• Mi smo kupili... = We bought..., not someone else.

This is because smo is a clitic. In Croatian, clitics usually go in the second position of the sentence or clause.

In this sentence, the first whole unit is:

Za rođendan

So the clitic smo comes right after that unit:

Za rođendan smo kupili...

If the sentence started with the verb instead, then you would get:

Kupili smo crveni balon...

Both are normal. The difference is mainly in word order and focus, not basic meaning.

In the Croatian past tense, the l-participle agrees with the subject in number and also, in many situations, gender.

Here:

• smo = we
• kupili = bought

For we, the participle can be:

• kupili = masculine plural or mixed group, and also the usual default when gender is not specified
• kupile = an all-female group

So the sentence as written is the normal default form: Za rođendan smo kupili...

If a group of women said it, they could say: Za rođendan smo kupile...

Because balon is a masculine inanimate noun, and in the accusative singular, masculine inanimate nouns usually look the same as in the nominative.

So:

• nominative: crveni balon
• accusative: crveni balon

This happens because the object of kupiti is in the accusative, but for masculine inanimate nouns, that accusative often has the same form as the nominative.

Compare that with a masculine animate noun, which would change:

• vidim psa = I see a dog

But with an inanimate noun:

• vidim balon = I see a balloon

Because vrpca is a feminine noun, and here it is the direct object, so it must be in the accusative singular.

For feminine nouns like vrpca, the accusative singular usually changes -a to -u:

• nominative: vrpca
• accusative: vrpcu

The adjectives must agree with the noun in gender, number, and case, so they also take feminine accusative singular endings:

• duga → dugu
• bijela → bijelu
• vrpca → vrpcu

So the whole phrase matches:

dugu bijelu vrpcu

The dictionary form is vrpca.

Croatian dictionaries normally list nouns in the nominative singular, so you would look up:

vrpca = ribbon

In the sentence, it appears as vrpcu because it is in the accusative singular as the direct object of kupili.

So:

• dictionary form: vrpca
• form used here: vrpcu

A learner often notices this because dictionaries usually give the adjective as crven.

In actual Croatian, the longer form crveni is very common before a noun:

• crveni balon

But after to be, you normally use the short form:

• Balon je crven.

So a very useful beginner rule is:

• before a noun: often crveni balon
• after je: balon je crven

The full grammatical explanation involves the old distinction between short and long adjective forms, but for everyday learning, that simple contrast is enough.

Croatian can place more than one adjective before a noun, just like English:

• dugu bijelu vrpcu = long white ribbon

Both adjectives must agree with vrpcu in gender, number, and case.

The order is not completely fixed, but some orders sound more natural than others. Here dugu bijelu vrpcu sounds normal and natural.

You could also hear:

• bijelu dugu vrpcu

but that may sound like the speaker is emphasizing the color differently.

So the order is somewhat flexible, but not random.

Because Croatian has no articles.

There is no direct equivalent of English a/an and the in ordinary grammar. Croatian usually leaves definiteness to be understood from:

• context
• word order
• stress/emphasis
• demonstratives such as ovaj, taj, onaj when needed

So:

• crveni balon can mean a red balloon or the red balloon
• the exact interpretation depends on context

If you want to be more specific, you can use a demonstrative:

• taj crveni balon = that red balloon
• ovaj crveni balon = this red balloon

This is about aspect, which is very important in Croatian verbs.

• kupiti = perfective → to buy, as a completed action
• kupovati = imperfective → to be buying, to buy habitually, repeatedly, or with focus on the process

In this sentence, the action is presented as completed:

we bought a balloon and a ribbon

So kupiti is the natural choice, and in the past tense that gives kupili.

If you used kupovali, it would suggest something like:

• we were buying
• we used to buy
• we were in the process of buying

So kupili fits a single finished purchase.

Yes. Croatian word order is fairly flexible, although not completely free.

The sentence as given is natural:

Za rođendan smo kupili crveni balon i dugu bijelu vrpcu.

You could also say:

• Kupili smo za rođendan crveni balon i dugu bijelu vrpcu.
• Crveni balon i dugu bijelu vrpcu smo kupili za rođendan.

These versions are still grammatical, but they shift the focus a little.

Very roughly:

• Za rođendan smo kupili... emphasizes the occasion
• Kupili smo... is a more neutral statement
• Crveni balon i dugu bijelu vrpcu smo kupili... emphasizes what was bought

So Croatian uses word order more for information structure and emphasis than English does.