Would the Spring Constant Change on the Moon?

Answer: on the moon, g is 1/6 times, but the extension of the spring also becomes 1/6 times since the mass now weighs only 1/6 of its weight on Earth. So the 1/6 in the numerator cancels out with the 1/6 in the denominator, and the period remains unchanged.

Is spring constant affected by gravity?

Gravity has nothing to do with the spring constant. It can only effect the net force on the spring depending on the orientation of the spring.

Do spring constants change?

The more compliant (or softer) the spring is the more it moves for the same amount of force. The spring constant is simply the inverse of the compliance and sometimes also called stiffness. The stiffer the spring, the less it moves or, conversely, the more force is required to get the same displacement.