"Do you not like scary movies?"
I don't understand why duolingo is using いや for dislike, when that is one of the more severe words for expressing distaste for something. I personally associate the word as something closer to the English word "repugnant" rather than dislike (好きじゃない)。
2020.5.4 いや「な」 in practice is used to say 'no' when you don't want to do something, or don't want something being offered.
"No, I don't want it." "No, I don't want to do it."
コーラはどう？イヤだ。 How about cola? No.
勉強しなさい！イヤだ。 Study! No.
On the flip side you can use it to ask if it's "not fine\not okay\disagreeable with you"
すしはイヤですか？ Is sushi not good with you?
運転してもらうのはイヤですか？ Would it not be okay if I have you drive? Is it bad if I have you drive?
So,怖い映画はイヤですか？ could be a person trying to decide what kind of movie to watch with a friend. The person could ask the friend like that.
Is a scary movie bad for you? Are scary movies a 'no'?
Then イヤな is also a noun adjective too.
イヤなおねがい a request I don't wanna do a horrible request
イヤな朝ご飯 a breakfast I don't wanna eat a horrible breakfast
Hope this is a bit helpful
怖い映画は好きではありませんか？ not accepted, even though surely it's the exact way to ask this. The given translation I would think means more like "Do you dislike/hate scary movies"? I don't like scary movies, but it doesn't mean I dislike them...
Edit: even weirder, it accepts the casual form of this 怖い映画は好きじゃない?
Second: いや (嫌) is a na-adjective meaning 'detestable, unpleasant, undesirable' and it's used for things that you're reluctant to see/touch/hear.
I guess they use a negative question in the translation because English language has limited means to convey the meaning of いや, or they would sound unnatural, such as "Are scary movies unpleasant to you?"
Acording to dictionary: "disagreeable, detestable, unpleasant, reluctant"