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 that of 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.
Youngs Modulus of steel is more than youngs modulus of rubber