1a.
Effectively the difference between decay 1 and decay 2 is the decay of the intermediate state which obeys the decaylaw dN/dt=-lambda*N which results in A(t)=lambda*N_0*e^{-lambda*t}.
1b.
The probability of reaching detector 1 or 3 is A and the probability of detector 2 is B. If the spins are aligned parallel to detector 1/3 A>B if the spins are aligned parallel to detector 2 B>A. Having said In this situation that means A²>A*B thus more detected events.