من تو را دیروز در اداره ندیدم.

Yes. In Persian, the verb ending often already shows the subject.

• ندیدم = I did not see
• The -م ending marks first person singular: I

So من is optional here.
The full sentence with من sounds slightly more explicit or emphatic:

• من تو را دیروز در اداره ندیدم. = I didn’t see you yesterday at the office.
• تو را دیروز در اداره ندیدم. = I didn’t see you yesterday at the office.

Both are natural.

را marks a specific direct object.

Here:

• تو = you
• تو را = you, as the object of the verb

Since دیدن means to see, the person being seen is the direct object, so Persian uses را:

• من تو را دیدم. = I saw you.
• من تو را ندیدم. = I didn’t see you.

For English speakers, را does not have a direct equivalent word in English. It is more of a grammatical marker than a word with its own meaning.

In spoken Persian, را is often pronounced رو:

• من تو رو دیروز در اداره ندیدم.

That is very common in everyday speech.

Because this sentence is in the simple past, not the present.

• ندیدم = I did not see
• نمی‌بینم = I do not see / I am not seeing

The sentence refers to yesterday, so Persian uses a past form:

• دیروز = yesterday
• therefore ندیدم fits naturally

So:

• من تو را دیروز در اداره ندیدم. = I didn’t see you yesterday at the office.
• من تو را نمی‌بینم. = I don’t see you / I can’t see you

ندیدم breaks down like this:

• نـ = negative marker
• دید = past stem of دیدن (to see)
• ـم = I

So:

• دیدم = I saw
• ندیدم = I did not see

This is a very common pattern in the Persian simple past:

• رفتم = I went
• نرفتم = I did not go

The dictionary form of the verb is دیدن = to see.

Persian verbs are conjugated using stems. For this verb:

• infinitive: دیدن
• past stem: دید

Then personal endings are added:

• دیدم = I saw
• دیدی = you saw
• دید = he/she saw

And with negation:

• ندیدم = I did not see

So the final ن in دیدن belongs to the infinitive form and disappears when the verb is conjugated.

Persian word order is flexible, but the default pattern is usually:

subject + object + time/place + verb

So this sentence is perfectly normal:

• من تو را دیروز در اداره ندیدم.

You can also move the time or place for emphasis:

• من دیروز تو را در اداره ندیدم.
• دیروز من تو را در اداره ندیدم.
• من تو را در اداره دیروز ندیدم. — less natural in many contexts, but possible depending on emphasis

The verb usually stays at the end.

A very common neutral order is:

• من دیروز تو را در اداره ندیدم.
• من تو را دیروز در اداره ندیدم.

Both are fine.

در is a preposition meaning in or at.

• در اداره = in the office / at the office

There is no ezafe here because اداره is the object of the preposition در.
So this is simply:

• در = in / at
• اداره = office

Together: در اداره

If you wanted to say something like the office’s manager, then you would use ezafe:

• مدیرِ اداره = the manager of the office

But in در اداره, no ezafe is needed.

Persian usually has no definite article like English the.

So اداره can mean:

• an office
• the office

The exact meaning depends on context.

In this sentence, English naturally says at the office, but Persian just says در اداره.
This is completely normal.

No. تو is the informal singular word for you.

Use تو for:

• friends
• family
• children
• people you know well

If you want to be polite or formal, use شما instead:

• من شما را دیروز در اداره ندیدم. = I didn’t see you yesterday at the office.

So the original sentence is informal in tone.

In standard Persian, with a specific direct object like تو, را is expected.

So the standard form is:

• من تو را دیروز در اداره ندیدم.

In casual speech, people usually do not omit it completely; instead they pronounce it as رو:

• من تو رو دیروز در اداره ندیدم.

That is the normal spoken version.

Leaving it out entirely can sound nonstandard or unclear, especially for learners.

A very natural spoken version would be:

• من تو رو دیروز تو اداره ندیدم.

Two common spoken changes happen here:

1. را → رو

   • تو را → تو رو

2. در → تو in everyday speech

   • در اداره → تو اداره

So:

• written / standard: من تو را دیروز در اداره ندیدم.
• spoken / casual: من تو رو دیروز تو اداره ندیدم.

Both mean the same thing.

Yes, it can.

Because Persian often drops subject pronouns, including من may make the subject more noticeable:

• من تو را دیروز در اداره ندیدم. = I didn’t see you yesterday at the office.

This can be useful if:

• you are contrasting with someone else
• you want to be explicit
• you are correcting someone

For example:

• علی تو را دید، ولی من تو را ندیدم.
• Ali saw you, but I didn’t.

So من is grammatical, natural, and sometimes slightly emphatic.