"My friend has a scientific question about the dance."
Translation:내 친구는 춤에 관한 과학적인 질문이 있어요.
관한 is the verbal modifier form (adjective form) of 관하다 (to be about). As the tips and notes from the Modifiers 1 skill suggest (accessible from mobile/desktop website), these verbal modifiers usually go in front of the noun they describe (personally I've never seen a case where it doesn't so I would say always is the rule with perhaps a few exceptions I've never seen). So in the example you provide, 춤에 관한 is describing the noun that comes afterwards, not 질문. If there is no noun it's ungrammatical I believe.
There is nothing wrong with your sentence grammatically but the meaning might change slightly.
(1) 에 관하여(서) = related to (= that has to do with topic).
-여(서) is primarily a conjunction = and then, and so
내 친구는 춤에 관하여(서) 과학적인 질문이 있습니다 = My friend refers to the dance and (so) raises a scientific question.
여(서) links two related ideas: 과학적인 질문이 있다 being consequential to 춤에 관하다.
(2) 에 관한 = relating to (= about the topic itself)
-ㄴ denotes a modifier (adjective)
내 친구는 춤에 관한 과학적인 질문이 있습니다 = My friend has a scientific question that is relating to the dance.
관한 acts as an adjective stacked on to the other adjective 과학적인. Both modify the noun 질문, i.e. 관한 과학적인 질문 = a question scientific and relating to
Korean and Japanese are very similar languages.
내 친구는 춤에 관한 과학적인 질문이 있어요.
→ 私の友達はそのダンスに関する (kansuru) 科学的な質問を持っています。
내 친구는 춤에 관하여 과학적인 질문이 있어요
→私の友達はそのダンスに関して (kansite) 科学的な質問を持っています。
Grammatically, there's a difference, but these two Japanese sentences have almost the same meanings.
I'm not a native English speaker or a native Korean speaker. So, I can't guess how a normal English speaker would translate these Korean sentences.