Elasticity is the capability of an object to return to its former shape once a load inducing strain is removed. If you were to drop a steel ball on a very hard surface it would probably bounce higher than than rubber. If you drop it on a softer surface because it would deform less then the surface it is to bounce off will be the one deforming so the bounce would be a function of the elasticity of the floor not of the ball.

A strand of silk is indeed stronger than a steel wire of the same diameter. The reason is that metal uses metallic bounds which is not as strong as the covalent bounds in a macro-molecule like the ones in silk. This also explains why Kevlar carbon fiber and carbon nanotubes are also stronger than steel.