1) We might observe exponential decay because of the exponential radiation decay of our nuclei. They decay according to the exponential decay, thus the nuclei number will go down according to exponential decay, so after some time we see just contribution from less nuclei because of this radioactive decay.
2) We observe count difference because we can see that probability along the spin direction is higher compared to probability in perpendicular direction. Thus it is logical that we will have more emissions along 3 detector direction.