As a korean, "My hobby is skateboarding." works too.
Not really. The whole sentence would be flipped.
Yeah, it can be flipped freely in that particular sense in both languages. I'm not sure if flipping it in Korean does more than shift emphasis, but that's all that really happens by doing it in English.
Is it possible to add "를" between "스케이트보드" and "타는"?
What is the purpose of 것이?
Indicating a gerund? From the past gerund lesson.