Hardness is a property that is commonly used to describe how resistant a mineral is to scratching. There is a well established hardness scale for minerals known as the Mohs' hardness scale- with 1 being assigned to the softest minerals and 10 for the hardest. The very softest can be scratched by a fingernail, harder minerals by a nail and knife. Luster refers to the appearance of light that is reflected from the surface of a mineral. Some minerals look 'dull' in luster, and some look 'shiny', for example.
Permeability is the ability of a rock or mineral to transmit fluids.
It is closely related to porosity, or how much open space is in-between particles of a rock. However, for a rock to be permeable, the pore spaces must be connected so that fluids can move through the rock. Porosity is the volume of open spaces in a rock. On the other hand, sandstone, which is formed by individual sand grains compacting together, generally has a high degree of porosity. Specific Gravity refers to how much something weighs in comparison to an equal volume of water.