Answer
See work below.
Work Step by Step
a. The mystery particle must be neutral, because charge is conserved.
The mystery particle must be a meson, because baryon number is conserved.
The mystery particle must only consist of up and down quarks (and antiquarks) to conserve strangeness, charm, topness, and bottomness.
Putting all of this together, the mystery particle is a $\pi^o$.
b. The mystery particle must be neutral, because charge is conserved.
This is a weak interaction. The mystery particle must be an antiparticle in the muon family because the muon lepton number is conserved.
Putting all of this together, the mystery particle is a $\overline {\nu}_{\mu}$.
