1) yes, it basically will find a non-optimal solution. At every point, the top of the ray looks for the bigger potential gradient, the charge in the surrounding volume grows, polarizing surrounding material (air, in this case) until a bigger gradient shows up and the ray continues over that direction. This is why the lightining path looks like a jigsaw; its basically a Monte Carlo search.
Not to say, that you can't apply this to find efficient solutions of the travelsman problem. This would require making a programmable configuration with weights related to capacitance so the electric arc finds the best path that also solves your particular adjacency matrix problem. This would probably be only hampered by the fact that the arc, in order to do any traversing, must burn its way across the capacitance barrier, so unless you find a cheap, repleaceable material that can also be configurable (the weight needs to adjust to the adjacency matrix weights) it will be cheaper to do this computation in a standard computer.
The lightning rod is based on two principles theorized by Benjamin Franklin. Lightning dissipation theory, and lightning diversion theory.
Lightning Dissipation Theory
This theory says that if you point a pointy metal object toward a polarized cloud, the metal object will be able to bleed off some of the energy from the cloud. Thus preventing a lightning strike.
This theory can actually be demonstrated, using a Van de Graaff generator and a nail. This YouTube video demonstrates the theory.
While this theory holds up on the small scale, it's been shown not to be effective at dissipating the large amount of energy built up in a storm. Fortunately, the design of the dissipation device (lightning rod) is also a great diversion device.
Lightning Diversion Theory
The lightning diversion theory says that if you provide a preferable path for the energy to travel along, there's a high probability the energy will follow that path.
Lightning rods are designed to be the highest objects around. This puts them closer to the polarized cloud, and reduces the distance the lightning must travel through the air. They are also made from conductive materials, and are connected to the earth through highly conductive materials. This provides a low resistance path to ground, making it a preferable path for lightning to follow.
While both theories hold up in the laboratory, only diversion theory seems to offer a viable lightning protection system.
Best Answer
Usually a building is equipped with a lightning rod that when strike by lightning, will conduct all the current to the ground. This is commonly known as grounding. As the wire conducts the lightning to the ground instead of passing it through the building, the inside of the building is very safe and will not experience any electrocution or fire.