If i remember well... The physical properties depend by the structure and the shape of the cristal, by the quantities of the other elements that could be found in the alloy.
Otherwise the mechanical properties need a test to be found because they are the results of the interaction of a sample of a specific material with the external world, such as: hardness, fatigue resistance and so on.
As u know and as Doc Chatterji said, the mechanical properties are a consequence of the physical properties.
The main hysical properties of solid matter are: (1) Mechanical properties: hardness, macroscopic elastic moduli etc. (2) Electrical properties viz. resistivity, magnetoresistance, superconductivity, Hall effect etc. (3) Magnetic properties viz. magnetic ordering and structure, hardness or softness of ferromagnetic material, hysteresis loop, coercivity, domain structure etc. (3) Dielectric properties viz. ferroelectricity, pyroelectricity etc. (4) Thermal properties viz. thermal conductivity, (5) Thermoelectric properties, (6) Magnetoelectric properties and many others. There are many other physical properties that are of interest. Please consult the text book of Kittel for example.
Yes color is a very important optical property. By knowing the color you can already have a good guess of many other properties. The color will immediately tell you whether the material is a metal or an insulator. It can tell you about the possible plasma frequency if metallic, it can tell you something about the valence state of the constituent atoms of the insulating compound especially when they are transition metal ions. The color change (under pressure for example) can tell you about valence or metal-insulator transition. So color is a very important property.