1-a) Why do you observe an exponential decay?
The decay of the intermediate state I follows the typical exponential decay curve.
1-b) Why is the number of events/counts for detector combination 1-2 smaller than for 1-3 ?
The radiation of the second photon will predominantly be emitted parallel to the nuclear spin. As detector 3 is across from detector 1, while detector 2 is perpendicular, a first decay being detected by detector 1 has a much higher probability of having a second decay being detected by detector 3.