Moja sestra je odlučila da ostane kod bake i dede.

Moja sestra is in the nominative case because it is the subject of the sentence.

• sestra = sister
• moja = my

The adjective/pronoun moja has to agree with sestra in gender, number, and case, so both are feminine singular nominative.

If you said moju sestru, that would be accusative, which is used for a direct object, not the subject.

Je is an unstressed auxiliary verb, and in Serbian these little unstressed words usually go in the second position of the sentence or clause.

So the neutral order is:

Moja sestra je odlučila...

Here, Moja sestra acts as the first unit, and je comes right after it.

This is a very common Serbian pattern with clitics such as je, sam, si, se, ga, mi, etc.

Je odlučila is the normal way to form the past tense in Serbian.

It consists of:

• the auxiliary je = is/has (here part of the past-tense structure)
• the past participle odlučila = decided

So Serbian past tense is often built like this:

• je odlučila = she decided
• je odlučio = he decided
• su odlučili = they decided

In everyday speech, speakers sometimes omit the auxiliary in some contexts, but the standard full form here is je odlučila.

Because the subject is feminine singular: sestra.

The past participle in Serbian agrees with the subject:

• odlučio = masculine singular
• odlučila = feminine singular
• odlučilo = neuter singular
• odlučili / odlučile = plural

Since sestra is feminine, the correct form is odlučila.

After verbs like decide, want, can, must, try, Serbian very often uses da + present tense instead of an English-style infinitive.

So:

• odlučila da ostane = decided to stay

This is one of the most important patterns in Serbian. English says to stay, but Serbian commonly says the equivalent of that she stays/remains, even though in English that sounds strange.

The infinitive ostati does exist, but after verbs like odlučiti, the da + present construction is very common and natural.

This is about aspect.

• ostati / ostane = perfective: to stay/remain as a completed decision or result
• ostajati / ostaje = imperfective: to be staying, to stay regularly, to keep staying

In this sentence, the idea is a single decision about what will happen, so Serbian uses the perfective verb:

• da ostane = to stay / to remain

If you used ostaje, it would sound more like an ongoing or habitual action, which is not the point here.

Here kod means something like:

• at someone's place
• with someone
• over at someone's house

So:

• kod bake i dede = at grandma and grandpa's place / with grandma and grandpa

This is a very common Serbian preposition when talking about being at someone's home:

• kod doktora = at the doctor's
• kod prijatelja = at a friend's place
• kod bake = at grandma's place

Because the preposition kod requires the genitive case.

So:

• baka → bake
• deda → dede

That is why you get:

• kod bake i dede

not

• kod baka i deda

Both nouns have to match the case required by kod.

Because one preposition can apply to both nouns when they are joined by i = and.

So:

• kod bake i dede = at grandma and grandpa's place

This is completely normal. Serbian does not need to repeat kod before each noun unless you want unusual emphasis.

Compare:

• kod bake i dede = normal
• kod bake i kod dede = possible, but sounds separate/emphatic, as if treating them more individually

Because Serbian does not have articles like English.

So Serbian does not normally say equivalents of:

• the sister
• a grandma
• the grandpa

Instead, definiteness is understood from context or shown in other ways.

In this sentence:

• moja sestra already tells you my sister
• bake i dede is understood from context as the relevant grandma and grandpa

This is very normal in Serbian.

Yes. Serbian often drops the subject when it is clear from context.

So you could also say:

Odlučila je da ostane kod bake i dede.

That means She decided to stay at grandma and grandpa's place.

The form odlučila already tells you the subject is feminine singular, so Serbian often does not need to say moja sestra unless you want to identify or emphasize who it is.

Yes, Serbian word order is more flexible than English, but not completely free.

The sentence you have is a very neutral and natural order:

Moja sestra je odlučila da ostane kod bake i dede.

You may also hear:

• Odlučila je da ostane kod bake i dede.
• Moja sestra je kod bake i dede odlučila da ostane.
  This is possible, but it changes the emphasis and sounds less neutral.

The biggest restriction is that clitics like je usually stay near the second position.

The letter č is pronounced like a strong ch sound, similar to the ch in church, but usually a bit firmer.

So odlučila is roughly:

od-loo-chee-la

More exactly:

• od = od
• lu = loo
• či = chee
• la = la

Also note that Serbian spelling is very phonetic, so once you know the letters, pronunciation is usually straightforward.