Does shaving your legs make your hair grow back faster?

Nope!

Think of your leg hair shaped like an upside down "V."

When you shave off the top, you're left with the thicker and darker bottom part of the hair. It could give the appearance of thicker and darker leg hair, but in reality it isn't.

Thats also why it is rougher, you're left with the sharper edges of the hair.