Ahh, your first question is the easy one! Light travels at the speed of light in vacuum, which is a constant. So there's no speeding up or slowing down.
Light "slows down" however when it travels through materials, like glass or water. In reality, photons are absorbed and re-emitted by the atoms of the material in which the light is traveling. You can work out the speed of light in a material by dividing the speed of light in vacuum (about 3 times 10^8 meters/second) by the refractive index of the material, which is around 1.4 for most kinds of glass, for example.
Light will react to a gravitational field and change its direction (again, not really "accelerating" -- Einstein tells us this effect comes from the fact that space and time are not "flat" and the light rays just follow the shortest distance between two points, which may be curved). When a photon travels into a gravitational potential, it picks up energy and changes color, becoming "blueshifted". On the way out, it becomes "redshifted" as it loses energy. An observer will always see the photon traveling at the speed of light as it reaches him, however.
Electrons move all the time. There are two kinds of "perpetual motion machines" -- machines in which the parts move all the time, and machines from which you can extract energy from it while leaving it in the original state. The first kind doesn't violate energy conservation or anything -- motion may continue indefinitely without adding or subtracting energy -- there's no "friction" for electrons in their lowest energy state orbits around atomic nuclei. There's also no average velocity of these electrons either, but if you were to make a measurement of the instantaneous speed of an electron in an atom at any instant of time, you will find it is moving.
What makes this all okay is that the electrons cannot lose energy if they are already in their lowest energy state. Quantum mechanics has the weird feature that there is such a thing as a lowest energy state, which is usually a tightly bound state where the electron is found close to the nucleus of an atom. Get it any closer on average, and you have to confine it to a smaller volume of space. Confining electrons to small volumes of space increases the expectation value of their speed (while reducing the electrostatic potential energy because opposite charges attract). At some happy equilibrium, the energy is minimized -- bring the electron in closer and it has to move more quickly, increasing energy, take it away, and the electrostatic potential energy is higher.
(published on 10/22/2007)