The best 3d location/vector method I've used allowed rotations using normal x,y,z coordinates, but you could do rotate an object in the xyz of the engine itself, the object, or the object that object was currently attached to. This made things like shooting a lob from a forward facing gun easy, since you could raise the shot from the gun rather than the world and no quaternions were involved. I don't know if quaternions were used underneath.
I don't understand what you mean, but I think you're describing exponential coordinates, or said another way, choosing an angular velocity and getting a rotation by following that angular velocity for a unit of time. https://en.m.wikipedia.org/wiki/Rotation_formalisms_in_three...