Learn Hardcore Farsi: تو آن دختر را دیروز در بازار دیدی؟ - Did you see that girl at the market yesterday?

In Persian, the verb ending often makes the subject clear. دیدی already means you saw (informal singular).
تو is still used when you want emphasis, contrast, or clarity (e.g., تو دیدی، من ندیدم = You saw it; I didn’t). In casual speech it’s often omitted.

Is this sentence formal or informal? How would I say it formally?

It’s informal, because it uses تو and دیدی (2nd person singular informal).
Formal/plural would be:

شما آن دختر را دیروز در بازار دیدید؟

What is را doing here?

را marks the definite/specific direct object. Here, آن دختر (that girl) is a specific person, so را is natural:

آن دختر را دیدی = you saw that girl
In everyday spoken Persian, را is usually pronounced ro (or o after vowels).

Can را be omitted?

Sometimes, especially in casual speech, but it can sound incomplete or less standard in writing. With a definite object like آن دختر, most speakers keep it (or at least say it as رو):

Colloquial: تو اون دختر رو دیروز تو بازار دیدی؟
Dropping it entirely can be possible in fast speech, but it’s not the safest learner choice.

Why is the object before the verb? Is that the normal word order?

Yes. Persian is typically S–(O)–(other parts)–V (verb at the end).
This sentence follows a very common pattern:

تو (subject) + آن دختر را (object) + دیروز (time) + در بازار (place) + دیدی (verb)

Can I move دیروز or در بازار somewhere else?

Yes, Persian word order is flexible, but the verb usually stays at the end. These are all possible with slightly different emphasis:

تو دیروز آن دختر را در بازار دیدی؟ (focus a bit more on “yesterday”)
تو در بازار آن دختر را دیروز دیدی؟ (less common, but possible) Most natural is what you have, or putting دیروز earlier.

How is دیدی formed (what tense is it)?

It’s simple past of دیدن (to see).

Past stem: دید-
Ending for you (informal singular): -ی
So: دیدی = you saw / did you see? (depending on intonation and punctuation)

How do you make it negative?

Add نـ to the verb:

تو آن دختر را دیروز در بازار ندیدی؟ = Didn’t you see that girl yesterday in the bazaar? / You didn’t see…?
If you want a neutral negative statement (not a question), drop the question mark and use normal statement intonation.

How is a yes/no question formed here? Do I need a word like “do/did”?

Persian doesn’t use an auxiliary like English do/did. You usually form yes/no questions with intonation (rising tone) and/or a question mark in writing:

تو ... دیدی؟
You can add آیا at the beginning for a more explicit/question-like feel (often more formal):
آیا تو آن دختر را دیروز در بازار دیدی؟

What’s the difference between آن دختر and این دختر?

آن = that (far from speaker / already mentioned / more “there/that one”)
این = this (near speaker / more immediate)
So:
تو این دختر را دیدی؟ = Did you see this girl?

Why does it say آن دختر (that girl) and not یک دختر (a girl)?

آن دختر is definite/specific: a particular girl the listener is expected to identify.
یک دختر is indefinite: any/one girl.

تو یک دختر را دیدی؟ can sound odd without context, because را
- یک often implies a specific-but-unnamed girl. A more neutral “Did you see a girl?” might be:
تو دیروز توی بازار دختری دیدی؟ (indefinite دختری = a girl)

How would this sound in everyday spoken Persian?

A very common colloquial version is:

تو اون دختر رو دیروز تو بازار دیدی؟
Changes:
آن → اون (that)
را → رو (object marker)
در → تو / توی (in)