It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.

yes

An even function is symmetric about the y-axis. An odd function is anti-symmetric.

Probably because polynomials and convergent power series in which all terms have even degree are even functions, and similarly for odd.

Basically, a knowledge of even and odd functions can simplify certain calculations. One place where they frequently appear is when using trigonometric functions - for example, the sine function is odd, while the cosine function is even.