It's not the same principle as a flammable gas detector. A gas detector works pretty much like a Davy lamp, with a gauze to stop ignition of the flammable gas. As you say, a heated catalyst is used as the sensor with flammable gas increasing the temperature and altering the resistance of the sensor.
A lambda sensor measures the difference in oxygen concentration between the exhaust gas and the atmosphere. The sensor material generates a voltage when heated and exposed to oxygen. This is similar to zinc-air batteries which generate a voltage when exposed to atmospheric oxygen.
Yes.
You should have looked for lambda sensors to get a decent article. Wikepedia is as crap as ever.
Do you think it does?