Ja nisam slobodan sutra.

No. In Serbian, subject pronouns are often omitted because the verb form already shows the person.

So:

• Ja nisam slobodan sutra.
• Nisam slobodan sutra.

both mean I’m not free / available tomorrow.

Including ja adds emphasis or contrast, for example:

• Ja nisam slobodan sutra, ali on jeste.
  I’m not free tomorrow, but he is.

In everyday speech, Nisam slobodan sutra is often the more natural choice unless you want to stress I.

Because the negative form of sam (I am) is a single word: nisam.

This comes from the verb biti (to be). In the present tense, the negative forms are:

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

So:

• Ja sam slobodan. = I am free.
• Ja nisam slobodan. = I am not free.

You should learn these as fixed forms.

Yes. Slobodan is an adjective, and in Serbian adjectives must agree with the person they describe in gender and number.

Here, slobodan is the masculine singular form, so this sentence sounds like it is spoken by a male speaker.

Common forms:

• slobodan = masculine singular
• slobodna = feminine singular
• slobodno = neuter singular
• slobodni / slobodne = plural, depending on the group

So:

• A man says: Nisam slobodan sutra.
• A woman says: Nisam slobodna sutra.

This is a very important feature of Serbian.

In this sentence, slobodan means free / available / not busy.

So Ja nisam slobodan sutra means something like:

• I’m not free tomorrow
• I’m not available tomorrow

The adjective slobodan can also mean free in other senses, such as not occupied, independent, or unrestricted, depending on context. But here the time word sutra makes it clear that it means not available tomorrow.

Yes. Serbian word order is fairly flexible, and moving sutra changes the emphasis more than the basic meaning.

All of these are possible:

• Ja nisam slobodan sutra.
• Sutra nisam slobodan.
• Nisam slobodan sutra.

They all mean roughly I’m not free tomorrow, but the focus shifts a bit:

• Sutra nisam slobodan. emphasizes tomorrow
• Nisam slobodan sutra. is very natural and neutral
• Ja nisam slobodan sutra. adds emphasis to I

Almost the same, but the adjective changes:

• Male speaker: Ja nisam slobodan sutra.
• Female speaker: Ja nisam slobodna sutra.

The verb nisam stays the same, but the adjective must match the speaker’s gender.

It is correct and natural, but in many situations Serbian speakers would simply say:

• Nisam slobodan sutra.

That is often the most everyday version.

If you want to sound a little softer or more polite, you might hear:

• Nažalost, nisam slobodan sutra.
  Unfortunately, I’m not free tomorrow.

So the full sentence with ja is fine, but not always necessary.

Yes. In many real-life contexts, that is exactly how a native English speaker would translate it.

For example, if someone invites you somewhere or asks for a meeting, Nisam slobodan sutra can mean:

• I’m not free tomorrow
• I’m not available tomorrow
• I can’t make it tomorrow

The Serbian sentence is simple, but the best English translation depends on context.

Because Serbian usually uses time expressions like sutra directly, without a preposition.

So you simply say:

• sutra = tomorrow

Examples:

• Dolazim sutra. = I’m coming tomorrow.
• Nisam slobodan sutra. = I’m not free tomorrow.

This is similar to English, where we also usually just say tomorrow, not on tomorrow.

A common way is to use da li:

• Da li si slobodan sutra? = Are you free tomorrow?
• Da li ste slobodni sutra? = Are you free tomorrow? (formal or plural)

In informal speech, people also often just use intonation:

• Jesi slobodan sutra?
• Slobodan si sutra?

So the sentence you have is useful as a model:

• Nisam slobodan sutra. = I’m not free tomorrow.
• Da li si slobodan sutra? = Are you free tomorrow?

The positive version is:

• Ja sam slobodan sutra.
  I’m free tomorrow.

Without ja, which is often more natural:

• Slobodan sam sutra.
• Sutra sam slobodan.

Notice that in affirmative sentences, the short form of to be often appears in the second position:

• Ja sam slobodan sutra.
• Sutra sam slobodan.

But in the negative, nisam is a single unit:

• Nisam slobodan sutra.