Breakdown of Они сказали, что сами сшили эти шторы.
они
they
этот
this [f: эта, n: это]
сказать
to tell, to say
что
that (conjunction)
Questions & Answers about Они сказали, что сами сшили эти шторы.
Why do we use сами here instead of себя for "themselves"?
Себя is a reflexive pronoun used when the action is done to oneself (like "they hurt themselves"). Сами is an emphatic pronoun used to stress that they did it on their own, personally, without help from anyone else.
Where is the subject in the second half of the sentence? Shouldn't it be что они сами сшили?
You absolutely can say что они сами сшили. However, because они (they) is already the subject of the first part (Они сказали), it is very common and natural in Russian to drop it in the second part. The plural forms of сами and the verb сшили make it completely clear who did the sewing.
Why is the perfective verb сшили used instead of the imperfective шили?
We use the perfective сшили because the focus is on the completed result. They did not just spend time in the process of sewing; they successfully finished making these specific curtains.
What case is эти шторы (these curtains)?
It is in the accusative case because it is the direct object of the verb сшили. For inanimate objects in the plural, the accusative case ending looks exactly the same as the nominative (dictionary) case.