How do you calculate the lowest price at a supermarket in order to save the most money?
You divide the price of each product by the size and therefore you can normalize the price per a specific unit size and compare each product. This will save you money!
Why is taking integrals and derivates and learning about limits and studying how functions change over time important?
Every industry uses some form of calculus, from physics and math to economics and even everyday life. From estimating sales for an upcoming year, or calculating arrival time on a road trip, all these actions require calculus.
What happens if you and your twin are separated and your twin takes a spaceship to the moon at near the speed of light (3X10^8 m/s)? How will your ages relate? Why is this important?
Your space and time are distorted relative to each other. It is amazing that you both will experience a different experience and your twin will come back younger than you. This is the basis for modern day technology and so much of modern science. The speed of light must be the same in all reference frames. From this, we can discover so much, such as the relation of Energy and Mass in the famous E = mc^2