Do O2 sensors slowly go bad or do they break?

If the heater inside the sensor is working, the sensor part usually goes bad slowly. However, the newer air/fuel sensors are often called oxygen sensors and those are a different story. Had you included the year, make, model, and engine, we could have given you a more definitive answer.

That info must be a national security secret.

When O2 sensors go bad, they go. It is a sensitive electronic component designed to be in a high heat environment.

Depends the heater could go bad so it won't give readings untill engine warms up. Or they could just be dirty. Depends everything always wears out differently or if just flat out stops working.

Both. I've had one come apart on me and had several slowly go bad.