پدرم امروز در اداره مشغول نوشتن ایمیل است.

Because -م at the end is a possessive ending meaning my.

• پدر = father
• پدرم = my father

Persian often attaches possessive endings directly to nouns instead of using a separate word like my.

You could also say پدرِ من, but پدرم is more natural and common in everyday speech.

Persian word order is fairly flexible, but the most neutral pattern here is:

• subject
  • time
    • place
      • predicate

So:

• پدرم = my father
• امروز = today
• در اداره = at the office
• مشغول نوشتن ایمیل است = is busy writing an email / emails

The verb or main predicate usually comes at the end of the sentence.
You can move امروز for emphasis, but this version sounds natural and standard.

For example, these are also possible:

• امروز پدرم در اداره مشغول نوشتن ایمیل است.
• پدرم در اداره امروز مشغول نوشتن ایمیل است.

But the original sentence is the most straightforward.

در means in or at, and اداره means office, department, or sometimes government office, depending on context.

So در اداره means:

• in the office
• at the office

In English, we usually say at the office, but Persian uses در very naturally here.

In casual speech, some speakers might also say توی اداره, which is more conversational.

مشغول means busy, occupied, or engaged in.

So مشغول نوشتن ایمیل است literally means something like:

• is occupied with writing email
• is busy writing email

It emphasizes that the action is in progress and that the person is occupied with it.

This is a very common Persian pattern:

• مشغولِ کار است = He/She is busy working.
• مشغولِ خواندن است = He/She is busy reading.
• مشغولِ نوشتن ایمیل است = He/She is busy writing email.

After مشغول, Persian usually uses an infinitive / verbal noun rather than a finite verb.

So:

• نوشتن = writing / to write

The structure is basically:

• مشغول + infinitive + است

That is why the sentence does not say مشغول می‌نویسد.

Compare:

• پدرم امروز در اداره مشغول نوشتن ایمیل است.
  = My father is busy writing email today at the office.

• پدرم امروز در اداره ایمیل می‌نویسد.
  = My father writes / is writing email at the office today.

The first version highlights being occupied with the action. The second is a more ordinary verb sentence.

Yes. In careful pronunciation, there is usually an ezafe linking these words, even though short vowels are normally not written in Persian script.

You would typically pronounce it roughly as:

• mashghul-e neveshtan-e email ast

So the full structure is understood as:

• مشغولِ نوشتنِ ایمیل است

This is very normal in Persian writing: the ezafe is often present in speech but not shown in the spelling.

Because ایمیل here is being used in a general / non-specific way.

In Persian, را usually marks a specific direct object.

So:

• نوشتن ایمیل = writing email / writing an email / writing emails in a general sense

If you meant a particular, specific email, you would be more likely to say something like:

• مشغول نوشتنِ ایمیل را → not correct in this structure
• better: مشغول نوشتنِ آن ایمیل است = He is busy writing that email.
• or in a regular verb sentence: دارد ایمیل را می‌نویسد = He is writing the email.

So the absence of را here is normal and expected.

Yes. A very common alternative is:

• پدرم امروز در اداره دارد ایمیل می‌نویسد.

This also means that the action is in progress.

The difference is mainly nuance:

• مشغول نوشتن ایمیل است = he is busy writing email
• دارد ایمیل می‌نویسد = he is writing email

The first one emphasizes being occupied with the task. The second one is a straightforward progressive form.

Yes, both patterns can appear, but they feel a little different.

• نوشتنِ ایمیل sounds more explicitly like the act of writing email
• ایمیل نوشتن is also very common, especially in less formal or more everyday-style phrasing

So learners may encounter both:

• مشغولِ نوشتنِ ایمیل است
• مشغولِ ایمیل نوشتن است

Both are understandable. The sentence you were given uses the more clearly nominal نوشتنِ ایمیل structure.

A natural pronunciation would be approximately:

pedaram emruz dar edâre mashghul-e neveshtan-e email ast

A few notes:

• پدرم = pedaram
• امروز = emruz
• اداره = edâre
• مشغول = mashghul
• نوشتن = neveshtan
• است is often reduced in everyday speech

So in casual speech, the ending may sound more like:

... mashghul-e neveshtan-e email-e

rather than a fully pronounced ast.

Usually it suggests an action that is currently going on or that he is occupied with today at that time.

Because of مشغول, the sentence has an ongoing sense:

• He is busy writing email today at the office.

So it feels more like a current situation than a habitual fact.

If you wanted a more habitual meaning, Persian would more naturally use something like:

• پدرم در اداره ایمیل می‌نویسد.
• My father writes emails at the office.

So مشغول ... است strongly points toward an ongoing activity.