(a) Since the standard reduction potential of second reaction is greater than first reaction, the second reaction is feasible at cathode (reduction occurs at cathode).
i.e., H+(aq)+e−→12H2(g),E0=0.00V.
(b) In the mercury cell, as the overall redox reaction (i.e., Zn(s)+HgO(s)→ZnO(s)+Hg(l)) does not involve any ion whose concentration may change, the cell potential of mercury cell remains constant throughout its life.