Halam patlıcanları fırına koyar koymaz ben de köfteleri tavaya bıraktım.

In Turkish, family words often take a possessive ending instead of using a separate word for my.

• hala = paternal aunt
• halam = my paternal aunt

So the -m is the 1st person singular possessive suffix, meaning my.

A useful extra note:

• hala specifically means your father’s sister
• teyze means your mother’s sister

So halam is not just my aunt, but more specifically my father’s sister.

They are definite/specific direct objects, so they take the accusative case.

Breakdown:

• patlıcanlar = eggplants
• patlıcanları = the eggplants
• köfteler = meatballs
• köfteleri = the meatballs

In Turkish, a direct object usually takes the accusative ending when it refers to something specific or already identifiable.

Compare:

• patlıcan koydu = she put eggplant / some eggplant
• patlıcanı koydu = she put the eggplant
• patlıcanları koydu = she put the eggplants

So here, the sentence is talking about specific eggplants and specific meatballs.

Yes, in some contexts -ları / -leri can be ambiguous.

patlıcanları can sometimes mean:

• the eggplants
  or
• his/her/their eggplants

But in this sentence, the natural reading is the eggplants, because it functions as the direct object of koymak.

Turkish often relies on context to resolve this kind of ambiguity.

They are in the dative case, which often expresses direction toward something.

• fırın = oven
• fırına = into/to the oven
• tava = pan
• tavaya = into/to the pan

With verbs like koymak and often bırakmak when meaning put/place, Turkish uses the dative for the destination:

• masaya koymak = put on the table
• çantaya koymak = put into the bag
• fırına koymak = put into the oven

So:

• patlıcanları fırına koymak = put the eggplants into the oven
• köfteleri tavaya bırakmak = put/drop the meatballs into the pan

That y is a buffer consonant.

When a vowel-initial suffix is added to a noun ending in a vowel, Turkish often inserts y to make pronunciation easier.

• tava
  • -a becomes tavaya
• araba
  • -a becomes arabaya

Without the buffer consonant, two vowels would clash.

koyar koymaz is a very common Turkish structure meaning as soon as ... or the moment ....

Pattern:

• verb stem + aorist
• then the same verb in a negative form: -maz / -mez

So:

• koyar koymaz = as soon as she/he puts
• gelir gelmez = as soon as she/he comes
• duyar duymaz = as soon as she/he hears
• biter bitmez = as soon as it finishes

It is basically a fixed time-expression pattern showing immediate sequence.

So the idea is:

• first action happens
• second action follows immediately

Because in koyar koymaz, the form is part of a set construction, not a normal tense choice.

Even though the whole event happened in the past, Turkish still uses this fixed pattern:

• koyar koymaz
• gelir gelmez
• oturur oturmaz

The actual time of the sentence is mainly carried by the main verb:

• bıraktım = I put / I placed

So the clause with koyar koymaz means as soon as she put..., even though it does not look like a regular past-tense form.

Here de means also / too.

So ben de means:

• I too
• I also
• sometimes and I, too

It is written separately because this de is a separate word, not a suffix.

Compare:

• Ben de geldim. = I came too.
• Evde kaldım. = I stayed at home.

In the second example, -de is a suffix meaning in/at/on, so it is attached to the noun. But in ben de, de means also, so it is separate.

Often yes. Turkish frequently drops subject pronouns when they are clear from the verb.

So something like this could also work:

• Halam patlıcanları fırına koyar koymaz, ben de köfteleri tavaya bıraktım.
• Halam patlıcanları fırına koyar koymaz, köfteleri tavaya bıraktım.

Adding ben makes the subject more explicit and can add a slight sense of contrast or balance:

• my aunt did this, and I did that too

So ben is not strictly necessary for grammar, but it is natural and useful for emphasis.

Both can be possible in many contexts, but they are not exactly the same.

• koymak = to put, place
• bırakmak = to leave, set down, put down, sometimes drop/place

In cooking contexts, tavaya bırakmak can sound like placing or dropping something into the pan, while tavaya koymak is a bit more neutral, simply put into the pan.

So bıraktım gives a slightly different nuance:

• a more physical set down / dropped into place feeling

Not a huge difference here, but it is a natural verb choice.

The default Turkish word order is usually Subject – Object – Verb, and this sentence follows that pattern inside each clause.

First clause:

• Halam = subject
• patlıcanları = object
• fırına = destination
• koyar koymaz = verb expression

Second clause:

• ben de = subject/topic
• köfteleri = object
• tavaya = destination
• bıraktım = verb

So Turkish usually keeps the verb near the end.

Also, the as soon as clause comes first, which is very natural in Turkish:

• Halam patlıcanları fırına koyar koymaz ...
• then the main action follows

Yes, Turkish word order is flexible, but changes usually affect emphasis rather than basic meaning.

The given version is very natural and neutral.

For example, Turkish can move words around to emphasize a destination or an object, but the standard learner-friendly pattern is the one you see here:

• time clause first
• then main clause
• verb near the end

So even though other orders may be possible, this sentence is a good model of normal Turkish structure.