Moja sestra sada radi, ali sutra nije na poslu.

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

• sestra is feminine singular
• so the possessive my becomes moja

Compare:

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

So moja sestra is the correct feminine form.

Radi is the 3rd person singular present tense of raditi.

Here it means:

• works
• or is working

In Serbian, the present tense often covers both:

• a general/habitual meaning: She works
• an action happening now: She is working

Because the sentence also includes sada (now), the meaning is clearly She is working now.

Serbian usually does not need a special continuous tense like English am/is/are + -ing.

Instead, Serbian normally uses the present tense plus context words if needed:

• sada radi = she is working now
• radi svaki dan = she works every day

So one Serbian present form can correspond to either works or is working in English.

Yes. Sada means now, and sad is a very common shorter variant.

Both are correct:

• Moja sestra sada radi.
• Moja sestra sad radi.

In everyday speech, sad is extremely common.
Sada can sound a little fuller or slightly more careful, but both are normal.

Because ali means but, and in Serbian it normally introduces a new clause, so it is separated by a comma.

• Moja sestra sada radi, ali sutra nije na poslu.

This is very similar to English:

• My sister is working now, but tomorrow she is not at work.

So the comma is standard punctuation here.

Serbian can use the present tense of a state with a future time word like sutra (tomorrow) to talk about a planned or expected future situation.

So:

• sutra nije na poslu = tomorrow she is not at work

This is natural Serbian.

You could also hear:

• sutra neće biti na poslu = tomorrow she will not be at work

That version is more explicitly future.
But sutra nije na poslu is also perfectly normal, especially when the future time is already clear from sutra.

With the verb biti (to be), the negative forms are written as single words:

• nisam = I am not
• nisi = you are not
• nije = he/she/it is not
• nismo = we are not
• niste = you all are not
• nisu = they are not

So nije is the correct form for she is not.

Na poslu means at work.

Literally:

• na = on / at
• poslu = the locative form of posao (job, work)

In Serbian, na poslu is the standard expression for being at one’s workplace or on the job.

It is just the natural idiomatic phrase:

• On je na poslu. = He is at work.
• Nisam na poslu. = I’m not at work.

Even though na often means on, here you should learn na poslu as a set expression meaning at work.

Because after na when it means location, Serbian uses the locative case.

The base noun is:

• posao = job / work

But after na in a location phrase, it becomes:

• na poslu = at work

So:

• nominative: posao
• locative singular: poslu

This kind of case change is very common in Serbian:

• u gradu = in the city
• na stolu = on the table
• na poslu = at work

They are related, but not identical.

• radi = is working / works
• je na poslu = is at work

Someone can be na poslu without actively radi-ing at that exact second. For example, they may be on a break, talking to someone, or just present at the workplace.

In your sentence:

• sada radi emphasizes that she is working now
• sutra nije na poslu says that tomorrow she will not be at work at all

So the two parts are not exact repeats; they express slightly different ideas.

Yes. Serbian word order is fairly flexible, because endings and context often show the grammatical relationships.

For example, these are all possible, depending on emphasis:

• Moja sestra sada radi, ali sutra nije na poslu.
• Sada moja sestra radi, ali sutra nije na poslu.
• Moja sestra radi sada, ali sutra nije na poslu.

The original version is very natural and neutral.
Changing the order usually changes emphasis, not the basic meaning.

Because Serbian usually does not need a subject pronoun when the subject is already clear.

Here the subject is already stated:

• Moja sestra

So adding ona would usually be unnecessary:

• Moja sestra sada radi... is enough.

You might add ona only for emphasis or contrast:

• Moja sestra sada radi, ali ona sutra nije na poslu.

But in a normal sentence, Serbian prefers to avoid unnecessary pronouns.

Yes, it is natural and correct.

It sounds like normal standard Serbian:

• Moja sestra sada radi, ali sutra nije na poslu.

A speaker might also say:

• Moja sestra sad radi, ali sutra nije na poslu.

That version sounds a bit more conversational because of sad instead of sada, but both are perfectly normal.