Answer
a. 60.7 GeV.
b. One is $\tau^+$ and the other is $\tau^-$.
c. No.
Work Step by Step
a. Calculate the energy released.
The Q-value is the mass energy of the reactant(s) on the left side, minus the mass energy of the products on the right side.
$$Q=m_{H^0}c^2-2m_{\tau}c^2=125\times10^3 MeV-2(1777MeV)$$
$$=121.4\times10^3MeV=121.4 GeV$$
By symmetry, each $\tau$ receives half of this released kinetic energy, so the KE of each tau lepton is 60.7 GeV.
b. The Higgs boson has no charge, so one $\tau$ is positively charged, and the other is negatively charged.
c. This is not possible. The mass of the two Z bosons (two times 91.2 GeV) would be greater than the mass of the Higgs boson (125 GeV). The proposed decay would not conserve mass-energy.
