Learn Farsi: تکلیفِ من تمام است.

While mashgh specifically refers to school homework like practice or handwriting, takleef is a broader word meaning "duty," "task," or "assignment." It is very commonly used in schools for homework, but it can also refer to general adult responsibilities.

Would a native speaker say tamaam ast in casual conversation?

Not usually. This sentence is in formal, written Farsi. In everyday spoken Farsi, the "aa" sound in tamaam changes to "oo", and the verb ast attaches to the word as a short "e" sound, making it sound like tamoome (تمامه).

Could I use an attached ending for "my homework" instead of takleef-e man?

Yes, you can! Saying takleef-am (تکلیفم) using the attached pronoun -am is actually much more common in spoken Farsi than using the independent word man with the ezafe connector. Both mean exactly the same thing.

Why does the sentence use ast (is) rather than a past tense verb for "finished"?

Because tamaam acts as an adjective here meaning "complete" or "entire." The sentence literally translates to "My homework is complete," which describes its current state. If you wanted to express the action of having finished it, you would use the compound verb tamaam kardam (I finished).