Yes, if by centre of the world you also think about rotation. Which direction us up and down (and left and right and front and back) also depends on a.
Yes, if by “position CFrame” you mean just CFrame, which includes both position and rotation. It gives you where b is in relation to a.
Yep
Nope, not at all. VectorToObjectSpace(v) always returns a vector that has the same length as v, PointToObjectSpace doesn’t. Check out this page for more info: CFrame | Documentation - Roblox Creator Hub