Budući da moja sestra peče tortu, ja ću kupiti svjećice i sok.

Here budući da means since, as, or because.

So:

• Budući da moja sestra peče tortu... = Since my sister is baking a cake...

Even though budući can look related to future in other contexts, in the fixed expression budući da it does not mean that something is in the future. It functions as a conjunction introducing a reason.

It is fairly common and a bit more formal or written-sounding than jer, but still completely natural.

Because Budući da moja sestra peče tortu is a subordinate clause, and it comes before the main clause:

• subordinate clause: Budući da moja sestra peče tortu
• main clause: ja ću kupiti svjećice i sok

In Croatian, when this kind of clause comes first, it is normally separated from the main clause by a comma.

Because moja has to agree with sestra in gender, number, and case.

• sestra is feminine singular nominative
• so the possessive adjective must also be feminine singular nominative
• therefore: moja sestra = my sister

Compare:

• moj brat = my brother
• moja sestra = my sister
• moje dijete = my child

Peče is the 3rd person singular present tense of peći.

So moja sestra peče tortu can mean:

• my sister bakes a cake
• my sister is baking a cake

In this sentence, the natural English meaning is usually is baking a cake, because it gives the reason for the later action: since she is baking a cake, I will buy candles and juice.

Croatian present tense often covers both the simple present and the present progressive, and the exact English translation depends on context.

Because tortu is the accusative singular form, used for the direct object.

• nominative: torta = cake
• accusative: tortu = cake, as the thing being baked

So:

• Torta je velika. = The cake is big.
• Peče tortu. = She is baking a cake.

This is a very common pattern for feminine nouns ending in -a:

• knjiga → knjigu
• kava → kavu
• torta → tortu

They are also in the accusative, but different noun types form the accusative differently.

svjećice

This is feminine plural, and for these inanimate nouns, the accusative plural is often the same as the nominative plural:

• nominative plural: svjećice
• accusative plural: svjećice

sok

This is masculine singular inanimate, and masculine inanimate nouns usually have accusative = nominative:

• nominative: sok
• accusative: sok

So all three objects are in the accusative, but they look different because of their gender and number.

A useful contrast:

• vidim sok = I see juice
• vidim psa = I see a dog

Masculine animate nouns usually change in the accusative, while masculine inanimate nouns usually do not.

Svjećice is a very natural word for little candles, especially birthday candles for a cake.

• svijeća = candle
• svjećica = little candle / birthday candle
• svjećice = candles, especially the small ones you put on a cake

So in this sentence, svjećice sounds especially appropriate because there is a cake involved.

This is the normal future I construction in Croatian:

• a form of htjeti used as an auxiliary: ću
• plus the infinitive: kupiti

So:

• ja ću kupiti = I will buy

Other forms are:

• ću = I will
• ćeš = you will
• će = he/she/it will
• ćemo = we will
• ćete = you will
• će = they will

Example:

• Kupit ću sok.
• Ja ću kupiti sok.

Both mean I will buy juice.

Because ću is a clitic, and clitics usually go in the second position in the clause.

So in:

• ja ću kupiti svjećice i sok

the first element is ja, and ću comes right after it.

That is why ja kupiti ću sounds wrong.

You may also see:

• Kupit ću svjećice i sok.

Here the future auxiliary comes after the infinitive form written as kupit. That is also standard Croatian.

Yes, it could be omitted.

Croatian often drops subject pronouns when they are clear from the verb form. So:

• Ja ću kupiti svjećice i sok.
• Kupit ću svjećice i sok.

Both mean I will buy candles and juice.

Including ja usually adds a little emphasis, contrast, or clarity. For example, it can suggest something like:

• My sister is baking the cake, and I will buy the candles and juice.

So the pronoun is not required, but it can be useful for emphasis.

Yes, Croatian word order is relatively flexible, though not completely free.

These are all possible with slightly different emphasis:

• Budući da moja sestra peče tortu, ja ću kupiti svjećice i sok.
• Budući da moja sestra peče tortu, kupit ću svjećice i sok.
• Ja ću kupiti svjećice i sok budući da moja sestra peče tortu.
• Kupit ću svjećice i sok budući da moja sestra peče tortu.

The basic meaning stays the same, but the emphasis shifts depending on what comes first.

One thing that does stay important is clitic placement, so forms like ja kupiti ću are still incorrect.

This is an aspect question.

• kupiti is perfective: to buy, as a completed action
• kupovati is imperfective: to be buying / to buy habitually / to do shopping

In this sentence, the speaker means a single completed future action:

• I will buy the candles and juice

So kupiti is the natural choice.

If you used kupovati, it would sound more like an ongoing or repeated activity, which does not fit as well here.