You got it!
Actually, I know nothing about Swedish, but yes, that's how this works in Ukrainian. You can add it to any question word: хто-небудь, що-небудь, яку-небудь (Дай мені ручку. Яку? Яку-небудь.)
There's actually another way to make all these constructions: будь. Будь-де, будь-коли, будь-чиї. And so on. But you really probably only need to know one.
I'm not sure I understand. Are you suggesting "I work anywhere" is wrong?
I agree that it does sound somewhat odd, but it's not technically wrong and there are contexts in which it would make sense: "Since the recession started, where have you been working?" "I work anywhere." (The implication being that this person will do anything to get a paycheck.)
More important is the way nunes89 grasped the grammatical function of "небудь," which was undoubtedly correct.
It would sound incorrect to English ears. You'd have to say "I would [I'd] work anywhere." Or I will work anywhere. Or I should work anywhere. You cannot currently work anywhere. You have to work somewhere currently. Just like, it cannot be, "I'm eating anything right now." I must be "eating something." Anyway, this is a Ukrainian course, not an English one. I just didn't want Swedish misunderstanding of English complicate the Ukrainian.