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In my opinion, the usage of だ is already correct in the following sentence.
But someone in my other questions said it is incorrect.

For example,

  * 映画を見ることが好きだ女性は私の妹です。The woman who likes watching movies is my younger sister.

  * 使い方が便利だ電気機は何ですか。 What is the electric appliance that is handy to use?

For the sake of completeness and comparison, I provide relative clauses with a
verb, i-adjective and noun as follows. I think they are also correct.

  * a verb: 映画を見ている女性が誰ですか。Who is the woman watching a movie?

  * i-adjective: 物価が安い町に住みたいです。I want to live in a town whose living cost is cheap.

  * noun: ジェットさんが２０歳だ映画を見ています。I am watching a movie in which Mr. Jet was 20 years old.

Must I change every だ to な in the given examples above? Please correct me if
it is wrong.
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grammar
Must a relative clause with な adjective be ended with な rather than だ?
You seem to be misunderstood about this and it is indeed a fairly common
misconception.

> 「na-adjective + だ」

In na-adjectives, the 「～～だ」 form is the 終止形{しゅうしけい} (predicative form),
meaning it is used to **_end_** a sentence. Thus, it **cannot** be used to end
a relative clause in front of its final noun.

> 「na-adjective + な」

This is the 連体形{れんたいけい} (attributive form), meaning it is always followed by a
noun. Thus, this is the form to use to end a relative clause since a relative
clause will always end in a noun.

(Was it not you whom I explained this to only yesterday? With 「便利な」?)

* * *

* * *

Now, let us go over your sentences.

「映画を見ることが好き **だ** 女性は私の妹です。」

Incorrect. It is 「好きな」.

* * *

「使い方が便利 **だ** 電気機は何ですか。」

Incorrect. Again, な ＞ だ

* * *

「映画を見ている女性 **が** 誰ですか。」

Incorrect. Definitely, は ＞ が. A **_very_** common mistake among J-learners.
Many use 「が」 as if it were the default subject marker, but it is not.

* * *

「物価が安い町に住みたいです。」

Correct.

* * *

「ジェットさんが２０歳 **だ** 映画を見ています。」

Incorrect. I wanna scream 「『だ』はsentence ender **だ** ！」.

You could say 「ジェットさんが２０歳 **の時の** 映画を見ています。」

or 「ジェットさんが２０歳 **だった時の** 映画を見ています。」
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Yes, you do have to change it.

It is ungrammatical for だ to appear at the end of a relative clause. If you
need to have a (present-tense) copula at the end of a relative clause, it must
be changed to either な or の. Which of these it changes to will depend on the
noun attached to it---some turn into into な (like 好き or きれい), some turn it
into の (like 普通 or 緑), and some can turn it into either な or の (like 特別).

> この映画が好き **だ** → 好き **な** 映画(を見る)  
>  この花は緑 **だ** → 緑 **の** 花(を摘んだ)

The former group is where the term "na-adjective" comes from. Which group a
given word falls into isn't really predictable. [(See this question for more
detail)](https://japanese.stackexchange.com/q/920)

However, only だ must be changed in relative clauses. Past-tense だった can remain
as it is in a relative clause.

> この映画が好き **だった** → 好き **だった** 映画(を見る)
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