مدیر امروز مشغول نوشتن یک ایمیل است.

Because Persian is usually verb-final. In this sentence, the main verb is the copula است (is), so it comes at the end.

A rough breakdown is:

• مدیر = the manager / a manager
• امروز = today
• مشغول نوشتن یک ایمیل = busy writing an email
• است = is

So Persian is organizing the sentence more like:

• The manager today busy writing an email is.

That final است is completely normal.

مشغول ... است means is busy ..., is occupied with ..., or very naturally in many contexts, is in the middle of ....

So:

• مشغول نوشتن است = is busy writing

This is a very common Persian pattern:

• مشغول خواندن است = is busy reading
• مشغول کار است = is busy working
• مشغول صحبت است = is busy talking

It often emphasizes that someone is engaged in an activity, not just that the activity is happening.

Because after مشغول, Persian normally uses an infinitive / verbal noun such as نوشتن (writing / to write), not a fully conjugated verb.

So Persian says something structurally closer to:

• is busy writing not
• is busy he writes

That is why you get:

• مشغول نوشتن است

rather than something like a direct equivalent of مشغول می‌نویسد.

Yes. In careful pronunciation, there is an ezafe after مشغول, and many speakers also pronounce a linking ezafe after نوشتن in this kind of phrase.

So the sentence is often pronounced approximately like:

• modir emruz mashghul-e neveshtan-e yek imeyl ast

But in normal Persian spelling, ezafe is often not written when the word ends in a consonant. So you see:

• مشغول نوشتن یک ایمیل

even though the spoken form may include those linking sounds.

Persian does not have a definite article like English the.

So مدیر can mean:

• the manager
• a manager

The exact meaning depends on context.

If the meaning shown to the learner is the manager, that is perfectly normal even though Persian does not use a separate word for the.

It can do both jobs.

In this sentence, یک ایمیل most naturally means:

• an email

But literally یک is also the number one.

So depending on context:

• یک ایمیل = an email
• یک ایمیل = one email

Here it is most naturally functioning like an indefinite article.

Also, Persian sometimes omits یک when English would still say a/an, but using یک here is very natural.

Good question. There are two helpful reasons to notice here:

• یک ایمیل is indefinite
• it appears inside the phrase نوشتن یک ایمیل / نوشتنِ یک ایمیل, which is a verbal-noun structure, not a simple finite clause like he writes the email

In Persian, را usually marks a specific/definite direct object. Since an email is indefinite here, را is not expected.

Compare:

• مدیر یک ایمیل می‌نویسد. = The manager writes an email.
• مدیر ایمیل را می‌نویسد. = The manager writes the email.

So in your sentence, no را is normal.

Yes. That is also a natural sentence.

The difference is mainly one of focus:

• مدیر امروز مشغول نوشتن یک ایمیل است.
  • emphasizes that the manager is busy/engaged in the activity
• مدیر امروز دارد یک ایمیل می‌نویسد.
  • is a more direct progressive: is writing an email

In many situations, both are possible. The مشغول ... است version slightly highlights being occupied with the task.

Yes. Persian word order is flexible, especially with time words like امروز.

For example, these are all possible:

• مدیر امروز مشغول نوشتن یک ایمیل است.
• امروز مدیر مشغول نوشتن یک ایمیل است.

The difference is mostly about emphasis and information flow, not basic meaning.

A learner can safely treat both as natural, though the original sentence is perfectly standard.

A careful pronunciation is approximately:

• modir emruz mashghul-e neveshtan-e yek imeyl ast

A more everyday spoken version may sound reduced, for example:

• modir emruz mashghule neveshtane ye imeyle

A few common reductions in speech are:

• است often becomes -e
• یک often becomes یه / ye
• the linking sounds may run together smoothly

So what looks a bit formal on the page often sounds more connected and lighter in real speech.