Such a great explanation, I must say!In a literal sense, they all mean the same thing: "I am going to school".
There indeed are subtle differences in nuance. For example, "(나) 학교가" would probably be the most ordinary way of saying you are going to school' "(나) 학교 가는데" kinda sounds like "I am going to school, but why?" Then again, it could simply be used as "I am going to school", just as how "yeah" in English could be used in difference situations either to affirm something or to inquire something. "학교 갈거야" and "학교 간다" just like the previous two mean the exact same thing, but the former sounds like what you'd say if someone were to ask you "what are you gonna do now/then?" while the latter is more or less immediate and declarative, just simply "declaring" what you are about to do now. Hope this helps.