Forward voltage tolerance on an ordinary diode
Don't confuse the tolerance with the actual variation. For a good manufacturing line the variation will be much, much smaller than the guaranteed tolerance, so that almost all of the manufactured products will meet the specification and can be sold. Also, don't assume that the statistical distribution of values is uniform; most manufacturing processes produce a variation with a normal, or Gaussian, distribution.

You can't really make any assumptions that extrapolate from the values in the datasheet. If the datasheet says that the maximum forward voltage is 1.0 V at 1.0 A then that is all the information you have. You can buy a large quantity of parts and characterize them yourself, but the characteristics of a given common part number may vary significantly for different manufacturers or for the same manufacturer over time. Good circuits are designed to work in spite of these variations rather than depending on them.