How Unreal Engine figure out Rotation, Velocity, Transformation through coordinate system?

Don`t be scared, but this is how all 3d engines should calculate rotations:
v=zjMuIxRvygQ

This thing solves poles problem ie. gimbal lock. And it is easier to code once you know how to build transformation matrices.

However if you want to know how to use blueprints rotation and vector math, well it depends what you want to do.