Ja sada pišem pismo.

Yes. In Serbian, the subject pronoun is often omitted because the verb ending already shows who is doing the action.

• pišem = I write / I am writing

So Ja sada pišem pismo. and Sada pišem pismo. both work.

You usually include ja when you want to:

• add emphasis
• create a contrast

For example:

• Ja pišem, a on čita. = I am writing, and he is reading.

So in your sentence, ja is correct, but it is not always necessary.

Sada means now.

A very common shorter form is sad, which also means now.

So these are both natural:

• Ja sada pišem pismo.
• Ja sad pišem pismo.

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

Pišem is the 1st person singular present tense form of the verb pisati (to write).

So:

• pisati = to write
• pišem = I write / I am writing

Some other present-tense forms are:

• pišem = I write
• pišeš = you write
• piše = he/she/it writes
• pišemo = we write
• pišete = you (plural/formal) write
• pišu = they write

It can mean both, depending on context.

In Serbian, the present tense often covers both:

• I write
• I am writing

So Ja sada pišem pismo is naturally understood as I am writing a letter now, because sada makes it clear that the action is happening at this moment.

Without sada, pišem could be:

• a general statement: I write
• a current action: I am writing

Context decides.

Pismo is in the accusative singular, because it is the direct object of the verb pišem.

You are writing what?

• pismo = a letter

For this noun, the accusative singular looks the same as the nominative singular:

• nominative: pismo
• accusative: pismo

That happens because pismo is a neuter noun.

So even though the form does not change here, the function does:

• pismo as subject could be nominative
• pismo as direct object here is accusative

Because Serbian does not have articles like English a/an and the.

So:

• pismo can mean a letter
• pismo can also mean the letter

The exact meaning depends on context.

If you want to be more specific, you can add other words:

• jedno pismo = one/a letter
• to pismo = that letter
• ovo pismo = this letter

Yes. Serbian word order is much more flexible than English word order.

The neutral version is:

• Ja sada pišem pismo.

But you can also hear:

• Sada pišem pismo.
• Pišem sada pismo.
• Pismo sada pišem.

These versions do not all sound equally neutral. The word order changes the focus or emphasis.

For example:

• Sada pišem pismo. = emphasis on now
• Pismo sada pišem. = emphasis on letter (maybe contrasting it with something else)

So yes, the order can change, but the most neutral learner-friendly version is the one you were given.

Pisati is imperfective.

That matters because in Serbian:

• imperfective verbs are used for ongoing, repeated, or habitual actions
• perfective verbs are used for completed actions

Since Ja sada pišem pismo describes an action that is happening right now, the imperfective verb pisati is exactly what you want.

A related perfective verb is often:

• napisati = to write, to finish writing

Compare:

• Pišem pismo. = I am writing a letter.
• Napišem pismo. = more like I write up / finish writing a letter in the appropriate context

You generally do not use a perfective present tense to mean an action happening right now.

The letter š is pronounced like sh in shoe.

So:

• pišem sounds roughly like PEE-shem

A rough pronunciation guide for the whole sentence:

• Ja = ya
• sada = SA-da
• pišem = PEE-shem
• pismo = PEES-mo

This is only an approximation for English speakers, but it is a useful start.

It can be written in both Serbian scripts.

Latin:

• Ja sada pišem pismo.

Cyrillic:

• Ја сада пишем писмо.

Serbian normally uses both scripts, and they match very closely letter-for-letter.

Yes. Pišem jedno pismo is correct.

Compare:

• Pišem pismo. = I am writing a letter / the letter
• Pišem jedno pismo. = I am writing one/a letter

Adding jedno makes it more explicit that you mean one letter, or it can make the noun feel more indefinite.

In many situations, though, Serbian simply uses:

• pišem pismo

without any word corresponding to English a.

Because Serbian does not build the present progressive in the same way English does.

English distinguishes:

• I write
• I am writing

Serbian usually uses the simple present tense for both:

• pišem

Then Serbian relies on:

• context
• time words like sada
• verb aspect

So sada plus the imperfective verb pišem clearly gives the meaning I am writing now.

Yes, it is natural and correct.

However, in everyday conversation, a speaker might more often say:

• Sad pišem pismo.
• Pišem pismo.

because:

• ja is often omitted
• sad is very common in speech

So your sentence is perfectly good, just slightly fuller than the most casual spoken version.