Prošle godine moja sestra nije imala slobodnu nedelju u tom mesecu.

No. In Prošle godine, godine is not plural. It is the singular oblique form of godina used in this time expression.

That can be confusing because godine can also be a plural form in other contexts. Here, though, the whole phrase means last year, not last years.

A useful learner tip: memorize prošle godine as one chunk.

Because prošle godine is the normal Serbian time expression for last year.

Serbian often uses this pattern with time words:

• ove godine = this year
• prošle godine = last year
• sledeće godine = next year

So even if the words look very literal, the idiomatic English equivalent is simply last year.

Serbian does not use a separate word like English did in sentences like didn't have.

Instead, Serbian uses:

• a past-tense auxiliary based on jesam
• plus the l-participle of the main verb

Here:

• nije = negative form of the auxiliary
• imala = past participle form of imati

So nije imala is the normal way to say didn't have.

Because the subject is moja sestra, which is feminine singular.

In Serbian, the past participle agrees with the subject in gender and number:

• imao = masculine singular
• imala = feminine singular
• imalo = neuter singular
• imali / imale = plural

So:

• Moj brat nije imao... = My brother didn't have...
• Moja sestra nije imala... = My sister didn't have...

Because this is the direct object of imati.

The dictionary form is:

• slobodna nedelja

But after imati you need the accusative:

• slobodnu nedelju

Both words change because the adjective must agree with the noun in case, gender, and number.

So:

• nominative: slobodna nedelja
• accusative: slobodnu nedelju

This is a tricky word because nedelja can mean both Sunday and week, depending on context.

So slobodnu nedelju could be understood as:

• a free Sunday
• or a free week / a week off

Since you already have the meaning from context, use that meaning here. But as a learner, it is good to remember that nedelja is potentially ambiguous.

Here slobodnu means something like free from work or obligations.

The adjective slobodan / slobodna / slobodno can mean different things in different contexts, for example:

• free
• available
• vacant
• not busy
• off duty

In this sentence it means a free week/Sunday in the sense of time off, not free of charge.

Because Serbian uses u + locative to mean in when talking about location or a time frame.

So:

• u tom mesecu = in that month

Here mesecu is the locative singular form of mesec.

This phrase tells you the time period within which something happened or did not happen.

Because taj changes form depending on case.

• nominative: taj mesec = that month
• locative after u: u tom mesecu = in that month

So tom is simply the correct case form of taj here.

This is a very common Serbian pattern: the demonstrative, adjective, and noun all change to match the case.

Yes. Serbian word order is more flexible than English word order because case endings show the grammatical roles.

For example, these are all possible with different emphasis:

• Prošle godine moja sestra nije imala slobodnu nedelju u tom mesecu.
• Moja sestra prošle godine nije imala slobodnu nedelju u tom mesecu.
• U tom mesecu prošle godine moja sestra nije imala slobodnu nedelju.

The meaning stays basically the same, but the focus changes.

You could sometimes omit moja if the context already makes it clear whose sister you mean, but moja sestra is very natural and completely normal.

Serbian often leaves out words that are understood from context, but when you want to be clear or explicit, using moja is the straightforward choice.

So in this sentence, moja sestra is the natural way to say my sister.