A mole is just a number like "dozen", it's not a unit of measurement since it doesn't measure anything. A meter is a measurement of length, a second is a measurement of time, a gram is a measurement of mass, and a kelvin is a measurement of temperature, but a mole isn't a measurement of anything.
The text I have highlighted in bold is incorrect. Strength is not about elastic change. The correct definition for strength, from wikipedia, is:
So strength is about the ability to withstand forces without PERMANENT change e.g breakage. So hardness is one type of strength, just like tensile...