offset in measuring decomposition potentials
Ok I will answer your  last question first. If you have two identical electrodes(i.e. same electrode material), the cell potential will be zero and there won't be any issues there.

You have to use inert electrodes so that you are not measuring the dissolution of the electrode itself.

The one part I am not sure you understand properly is the current growing. You want to vary the potential until the current raises exponentially when continuing to sweep. This will be a very sharp rise that will be hard to miss.