I heard that electrons accumulate at points on metals, and this clearly explains the arcing phenomenon, but how does a microwave make an electron imbalance on the fork?
Those sparks are due to dielectric breakdown of air.
Microwaves are absorbed by metal and majority of it is reflected off with same phase, just like a mirror. However, because of this, there can be a large concentration of electric fields in some parts, it causes the massive potential difference that in turn lead to dielectric breakdown of air and the sparks you see.
I think this link explains it quite well and seems to be reliable: http://engineering.mit.edu/live/news/1041-why-cant-we-put-metal-objects-in-a-microwave
As for the second part of your question:
The electric field is strongest on sharp edges. Why? Well that has been asked and answered here: Why is electric field strong at sharp edges?
So yes, the concentrated oscillating electric field and resulting high electric field seems very plausible between the tines of the fork. That, in turn, causes the sparks.
Another related point worth noting is that the actual movement of electrons is considerably slower than build up of strong electric field. The electric field causes the dielectric breakdown.
The basic idea is that microwaves are a form of electromagnetic radiation-- light. That light consists of an oscillating magnetic and electric field component. By Faraday's Law of Induction, a magnetic field in flux induces a current in a conductor... so it is the non-conservative, induced electric field in the conductor that produces an emf that moves the electrons in the fork.
The energy produced in a microwave oven is at a macro-scale wavelength (on the order of centimeters), and leaves the emitter as a coherent wave - one wavelength, phase, and polarization. Despite the "stirring fan" and other measures, objects in the oven will still experience (relatively) orderly macro-scale radio waves and therefore exhibit macro-scale effects. Radio waves (including microwaves) will induce voltage differentials and electrical eddy currents in conductors. So, foil (being a good conductor) in a microwave will end up with charges accumulating here and there (dependent on shape and orientation with respect to the incident waves); voltages can be high enough to break down / ionize the air between points on the foil, and separated by sufficient distance to cause the visible sparking and arcing you see.
On the other hand, visible light is at a micro-scale wavelength (in the range of 500 nanometers). Ordinary light sources (daylight, incandescent, fluorescent, etc.) are essentially streams of photons of random wavelength, phase, and polarization(although fluorescent light occurs at more specific wavelengths, it's otherwise a random emission of photons). As such, there is no macro-scale order as occurs with the microwaves produced in a microwave oven, and there is therefore no possibility of corresponding macro-scale effects.
Even laser light, which is coherent (uniform wavelength, phase, polarization) is still at a micro-scale wavelength. It could generate a plasma (dislocating electrons, etc.), but purely due to heating effects. It won't produce a sparking/arcing effect because the wavelength is too short to produce an effect with such a large scale order (voltage differential over millimeters to centimeters).