Electricity and light are the same phenomenon: electromagnetism. Light is an electromagnetic wave, when we talk about the speed of light, we mean the speed of an electromagnetic wave in a vacuum (in space for example). In any other medium it is slower, how much slower depends on the characteristics of the medium: the electric permitivity and the magnetic permeability (these sort of tell you how hard it is to change either an electric or magnetic field in that medium).
When you send electricity down a wire to a light, it travels as an electromagnetic pulse/wave down the wire. The electrons dont actaully move down the wire very fast at all, several mm per minute or so, and for AC electricity there is no net displacement of electrons! The speed of an electromagnetic wave down a wire, or any other transmission line will be less than the speed in a vacuum. How much slower depends on the charateristics of the transmission line: for wire transmission lines say, it depends on their electrical properties inductance and capacitance. Inductance relates to how hard it is to create a magnetic field around the transmission line, capacitance electric field. The inductance of the transmission line will depend on the exact shape and configuration of the wire AND the permeability of the medium surrounding the wire. The capacitance also depends on the configuration of the wire and the permitivity of the medium. The actual speed of an electromagnetic wave in a transmission line (the propogation speed) could typically be an order of magnitude less than the speed of light. You could get it much slower if you wanted to as well.
Basically the same physics applies directly to light or electricity, because they are the same thing! But we know now from eistiens relativity that nothing can 'travel' faster than the speed of light in a vacuum: any medium (including electrical transmission lines) slow down the propogation of an electromagnetic wave (Infact if the wave travelled faster down the wire than the speed of light, some observers could see the bulb light up before the switch was flicked! This is why relativity postulates that the speed of light in a vacuum is the fastest anything may travel, other wise we have paradoxes: what if the electricty travelled faster than light, an observer noticed the light come on before the switch was flicked, then cut the wire before the switch was flicked? then how did the bulb get any power to start with?! But this cannot happen)
So the short answers to you r questions:
No, No, A very very long time and they may never get there at all, yes and yes. In that order.