(I)
The reason a mercury cell holds its voltage so steadily comes down to what is dissolved in it. A cell's voltage changes when the concentration of the reacting ions changes, because the potential follows those concentrations. In a mercury cell the substances taking part, zinc, mercuric oxide, and the products, are solids or are held in a thick paste rather than freely dissolved. Since nothing is building up or thinning out in solution as the cell runs, the ion concentrations stay effectively fixed. With nothing to shift the potential, the voltage stays almost the same right through the cell's working life.
(II)
A salt bridge is needed to keep the cell running. As the cell works, the half-cell where oxidation happens keeps gaining positive ions, and the half-cell where reduction happens keeps losing them, so each side starts to build up a charge. This charge imbalance would quickly stop the reaction. The salt bridge lets its own ions drift into each beaker to cancel that build up, keeping both sides electrically neutral, and it completes the circuit so current can keep flowing. It also separates the two solutions so they do not mix directly.
Final answer: (I) the reactants are solids/paste, so ion concentrations never change and the voltage stays constant; (II) the salt bridge keeps both half-cells neutral and completes the circuit so the cell keeps working.