To give you more detail, 상관없다 is a single adjective meaning something doesn't matter or the speaker doesn't care. As I see it, the verb-based phrase 상관 안 해요 (상관안해요 is not correct) has two related usages. One is in the same sense as 상관없어요, and the other is that the speaker will let someone do whatever they want (i.e. won't bother to interfere with their business; 상관하다 in this sense is similar to 간섭하다). The adjective-verb difference means there are cases where the two are not interchangeable. e.g. - 상관하지 마 = Don't interfere in my business. - 상관없지 마 (X) = ungrammatical - can't use -지 마(말다) on an adjective.

Yes. We use it. But you can use “상관안해요” like this. (Spacing words) -> 상관 안 해요.