For spells that have different versions of itself, like Manabolt and Manaball, do you need to learn them in any particular order, or can you learn a spell like Toxic Wave without Acid Stream?

Nope. You can learn the spells in any order, and don't need the preceding type to know the other.

Example: You can know Toxic Wave without Acid Stream.

Yeah. They're not levels of progression. They're just spells with similar sorts of effects.

It's the same as you don't need to learn "Pistol" before you can learn "Automatics" in the military.

Usually, they'll have you stripping and cleaning the Assault Rifle before you even touch a pistol.