Mixing liquids when applying a voltage
I won't comment on B for the moment, but liquid-liquid interface electrochemistry is quite a vibrant field. There's a review of it here, if you're interested. The simplest interaction involves ions: if one applies a potential across the interface of sufficient strength and polarity, the energy barrier of transferring a given ion from one phase to the other can be overcome. If you do this with something like a solvatochromic dye, it will change colour as it moves from one phase to the other. (It would have to be something that doesn't partition into the second phase easily on its own, of course) One could also have some reagent in one phase that reacts with the ion being pushed across the interface that produces some coloured product. (iodide-starch, perhaps?) There are also voltage-sensitive dyes, though I don't have any experience with them.

One thing to note is that neither water nor oils and other immiscible solvents are generally very conductive. To keep the cell resistance down to a reasonable level, it will be necessary to dissolve electrolytes in both. Things like Tetrabutylammonium hexafluorophosphate are commonly used as electrolyte in non-aqueous electrochemistry.