High voltage. 20 kV per cm to get a current through air.

Any electricity will have voltage and current. It's static electricity so doesn't have a frequency like an AC charge would. Voltage is very high at about a gigavolt (1,000,000,000 volts), with current around 50,000amps or so.

It's a high voltage earthing through your wiring, so i'd guess your fuses wouldn't blow as they're on the live side.

Lightning doesn't actually involve moving much charge, the damage is done by the rate of change.

It's a very high peak current attempting to pass through an apparently short bit or wiring, in a very short time. The voltage induced across that wire is all to do with the rate of change of current:

V = L.dI/dt.

Since the time is very short (single-figure microseconds) even though the instantaneous current is moderate (100 - 1000A) a meter or two of 'conducting wire of any thickness at 1microhenry a metre or so - results in very significant transient voltages appearing, easily enough to kill consumer electronics.

That's all there is to it, and since the causes are so fundamental in physical terms, there's really nothing you can do about it either. The best protection is to make structures that look likely to get hit.. have a low inductance to the Earth around the outside, a.k.a a Faraday cage; hence those flat, wide lighting 'tapes' you often see around the outside of most buildings (and which go to their own separate earth spikes).