Question

Are "That teacher is always shouting" and "This cake is the best thing ever" hyperboles?

Answer 1

The definition of a hyperbole is: exaggerated statements or claims not meant to be taken literally.

By saying a teacher is "always shouting", you are implying that a teacher yells often. This is an exaggeration. 

By saying this cake is the "best thing ever", you are also exaggerating.