Fastest observed biologically evolution rate?
Theoretically, it really depends how crazy you want your model to be! Also it depends what you mean by "evolution rate".

Let's consider a very simple and quite crazy model. Let's assume that by evolution rate you mean the difference between mean phenotype between one generation and the next. Let consider a trait (which heritability is $h_N = 1$) which takes only two values $x_1$ and $x_2$. In a given generation, half the individual carry the trait value $x_1$ and half the trait value $x_2$. If the relative fitness of $x_1$ and $x_2$ are 1 and 0 respectively, then the evolution rate is simply $| \frac{x_2 + x_1}{2} - x_1 |$. Allow $x_2$ and $x_1$ to be very big values and the rate of evolution will be very fast. In the most extreme case, $x_1 = \infty$, then the evolution rate is simply infinite.