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1a) I am not sure about the reason. Intuitively however, an exponential decay feels right. Maybe it has to do with the fact that within a certain time, the number of short events that can be measured is much larger than the number of long events (because in the time that a long event takes place, no short events are registered).
1b) (D = detector) Because D3 is positioned along the direction of nuclear spin. This direction is more likely to be the direction of the emitted gamma 2 ray than the direction along which D2 is positioned. D3 will therefore register more gamma 2 rays than D2.
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