In this case, for the reaction by which water is decomposed to molecular hydrogen and oxygen:
It is necessary to perform the inspection balance process since there is a dissimilar number of atoms of oxygen on both sides; therefore, by putting a 2 on water we balance oxygen:
But now, there are four hydrogens on the left; therefore, we put a 2 on hydrogen to finally balance it:
And obviously, the coefficient in oxygen is an unwritten 1.
It is false. The salt bridge is not a path for electrons, but a path for ions to flow from one half-cell to another. It help to balance the charge between the oxidation and reduction vessels.