Mechanisms of extracellular stimulation of neurons
Good question. Just to set some stuff straight: In contrast to a comment placed earlier, there is definitely a current flow between electrodes in neural tissue, as long as the impedance is not too high. The potential difference between the electrodes and impedance determines how much current flows, basically following Ohm's law: I = U/R.

As to your hypothesis (A) - I confirm  WYSIWYG's answer - electrodes indeed do not have to be coated, as long as they are conductive. For instance, Ag/AgCl coatings are used to electrically stabilize the electrode, mainly for sensitive reference electrodes used for recording purposes (see a commercial link here). For stimulation purposes chloride salts are a big no no, as AgCl or comparable chloride salts will be converted into metal (e.g. silver) + Cl2, obviously a toxic gas.

As to your hypothesis (B) - It is the electrical field that activates neurons (Basser &amp; Roth 2000) by means of inducing current flow. For example, imagine a cathode (negative electrode) placed close to a neuron. Normally in rest, a neuron's membrane is hyperpolarized (more negative ions inside the cell, the extracellular fluid can be considered to be neutral). The negative electrode will now cause the extracellular fluid to be negatively charged. Subsequently, positive current will flow out from the cell close to the electrode and into the electrode. According to Ohm's law, the membrane voltage is thus positive (note Ohm's law: U = IxR, with I being positive and R being always positive, means U is positive). Hence, the membrane is depolarized, as the resting state is a negatively charged state (hyperpolarized). With an anodic electrode neurons can also be depolarized but due to a slightly different mechanism. Basically, the flanking regions of the now negative current flow to the positive electrode become subject to positive current, as it counterbalances the negative flow to the electrode.  The chapter of two veterans in electrical stimulation, Abbas and Miller, in (Cochlear implants) is particularly helpful, as is (Basser &amp; Roth 2000). I can't link a pdf to Abbas and Miller, excuse me for that. I bet your university library will have access to it. Hope this helps.