The AL2O3 layer is very, very thin. A few microns. It doesn't corrode beyond this.
AL is a resonable conductor of electricity, just not as good as copper. It also expands more than copper does when heated. This is the reason why you need special termination compared to copper wiring, because of the higher thermal expansion of AL.
What likely happened with the desk lamp is a short was formed somewhere. As for charing up along a wall, unless the insulation caught fire from an arc short near a termination or between source and sink, or source and ground conductors in the wire somewhere...starting a wire insulation fire, there is no way the entire wire would get hot enough to cause that kind of damage unless you had a bad breaker. Even a simple thermal breaker would pop within just a couple of seconds at the kind of electrical load that would start that kind of fire, let alone a standard thermal/magnetic breaker, which should be set to pop at slightly above rated load for prolonged periods, or roughly double load for short periods.
A standard breaker is designed that way so that prolonged loads that might push the wiring above its rated temperature, generally 60C in house hold wiring, will trip the breaker after a minute or two of load. It also has a magnetic component that will trip when a transient load exceeds roughly double the rating on the breaker. This is to allow motor start up for things like AC compressors, power tools, air compressors, fridges, etc where the transient load might be significantly higher than the constant load. So when your 1200 watt vacuum cleaner first turns on and pulls 2500w from your 15 amp, 120v (1800w) outlet for a second or two, it doens't trip the circuit breaker. However, when there is an open short and suddenly 96000w is coursing through the wiring it'll pop the breaker almost instantly.