Learn Hardcore Turkish: Avukat, belgeyi imzalamanı özellikle istedi. - The lawyer especially asked you to sign the document.

Because the document is a specific, definite direct object of the embedded verb imzalamak. Turkish marks specific direct objects with the accusative -i/-ı/-u/-ü. Since belge ends in a vowel, a buffer -y- is added: belge-yi. If it were indefinite, you’d say:

bir belge imzalamanı = your signing a document (not a specific one)
belgeyi imzalamanı = your signing the (specific) document

How is imzalamanı built, and what do the endings mean?

It’s a nominalized verb (a “verbal noun”) used as the object of istedi:

imzala- = sign
-ma = nominalizer (turns the verb into a noun: “signing”)
-n = 2nd person singular possessive (“your”)
-ı = accusative case (because the whole phrase is the object of istedi) So imzala-ma-n-ı ≈ “your signing (it).”

Where is the word “you”? Why isn’t sen in the sentence?

“you” is encoded inside imzalamanı with the possessive -n (“your”). In full, you could say:

Avukat, senin belgeyi imzalamanı özellikle istedi. The genitive subject senin is optional and usually dropped when clear from context.

Why does imzalamanı take accusative -ı?

Because the entire nominalized clause (belgeyi imzalaman) is the direct object of istedi (“wanted/asked for”). In Turkish, when a nominalized verb functions as a direct object, it typically takes the accusative case.

Could I say imzalamayı instead of imzalamanı?

That would change the meaning. Without a genitive subject (like senin) and possessive on the verbal noun, Turkish assumes subject control by the matrix subject. So:

Avukat belgeyi imzalamayı istedi = The lawyer wanted to sign the document (himself). To say “wanted you to sign,” you need the possessive marking: imzalamanı (your signing).

What exactly does özellikle modify here, and can I move it?

Here özellikle (“especially/particularly/specifically”) most naturally modifies istedi, i.e., it was a specific/particular request. Acceptable variants with slightly different focus:

Avukat, özellikle belgeyi imzalamanı istedi. (focus on the wanting being special/specific)
Avukat, belgeyi özellikle imzalamanı istedi. (focus on the act of signing in particular, rather than doing something else with the document) Keep özellikle near what you want to emphasize. The original sentence emphasizes the request itself.

Is the comma after Avukat necessary?

It’s optional and used for readability/emphasis, marking Avukat as the topic. You can write:

Avukat belgeyi imzalamanı özellikle istedi. Both are fine.

How would I make this polite/formal “you” (plural or respectful)?

Change the possessive to 2nd person plural:

Avukat, belgeyi imzalamanızı özellikle istedi. If you include the explicit subject, use sizin:
Avukat, sizin belgeyi imzalamanızı özellikle istedi.

How do I say “he wanted him/her to sign” (3rd person)?

Use 3rd person possessive on the verbal noun:

Avukat, belgeyi imzalamasını özellikle istedi. = he wanted him/her to sign the document. Other persons:
“me”: imzalamamı
“us”: imzalamamızı
“them”: imzalamalarını

How do I say “he especially wanted you NOT to sign the document”?

Negate the verbal noun:

Avukat, belgeyi imzalamamanı özellikle istedi. Pattern: negative stem + nominalizer + possessive + case → e.g., gelmemeni, yapmamanızı.

Why is there a buffer -y- in belgeyi, but not in imzalamanı?

belge + i would create a vowel clash, so Turkish inserts buffer -y- → belgeyi.
In imzalamanı, the preceding segment ends in -n (the possessive), so no buffer is needed. You do see a buffer -n- with 3rd person possessive plus case: imzalaması (his/her signing) → accusative: imzalamasını.

Can I add senden (“from you”) to make “He asked you for this”?

Yes. It’s common to explicitly mark the addressee with ablative:

Avukat, senden belgeyi imzalamanı özellikle istedi. Here, senden is the person the request is directed to, while imzalamanı shows who is expected to perform the action (you). You can include both for clarity/emphasis.

Could I use a “that”-clause with ki instead?

Not with istemek in standard Turkish. You don’t say istedi ki.... Use the nominalized structure (-mA + possessive) as in the original, or a diye clause with an imperative for a more direct “asked (that you do X)” style:

Avukat, belgeyi imzala diye özellikle istedi. The nominalized form is more neutral/formal.

Does özellikle mean “especially,” “specifically,” or “particularly”?

All three can be good translations depending on context. Synonyms include bilhassa and özellikle itself is the standard choice. Avoid forms like özellikle olarak (unnatural).

Can you summarize the morphology of the key pieces?

belge-yi: document + accusative -i (with buffer -y- after a vowel)
imzala-ma-n-ı: sign + nominalizer -ma + 2sg possessive -n + accusative -ı
özellikle: especially/particularly
iste-di: want + past -di (3sg)