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a) The number of events depends on the half-life time of the intermediate state. At a time equal to the half-life time half of the nuclei at the intermediate level have decayed. At twice the half-life time 3/4 will have decayed. So only 1/4 will still have to decay. As you can see this goes in an exponential way.
b) Detector 3 has the same orientation as detector 1 and it is more likely that the nucleus emits a photon in the same parallel to its spin which is the same directin as detector 1 and 3 while detector 2 is perpendicular oriented to the spin of the nucleus.
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