1-a) The signal starts when a gamma_1 photon is detected. The nucleus is then in an intermediate state and needs to decay. As any nuclear ensemble follows an exponential decay in time, here it will be no different, so the stop detector will see this.
1-b) This has to do with the nuclear orientation. The anisotropy pattern (shaped like the infinity symbol) shows that there are more photons emitted the horizontal direction than in the vertical direction, causing more counts in combination 1-3 than 1-2.