Plenty of things. They keep the ecosystem in balance, provide us with food and other products, make great companions when they're domesticated...It goes on and on.
It is used in physics all the time. For example, acceleration is the derivative of velocity which is a derivative of position with respect to time. Calculating the amount of work done in a vector...
depends on your point of view. for example to me sound makes everything better like movies and of course music. but if u ask a deaf person they might not appreciate what they dont have. alot of...