That is what the check engine light is for. It informs you of a failure.
The "check engine" light would illuminate.
The O2 sensor is one of many things that can turn on the check engine light. You need to have it checked for codes.
Not likely. A bad O2 sensor would illuminate the check engine light and the engine performance would suffer.
Yes
If it has a downstream O2 sensor the check engine light will come on but if it does not the light may not come out. In most instances it will set the check engine light.
Check to see if the wiring is damaged.
The check engine light would illuminate and the code set would help lead you to which sensor is at fault.
Check engine light would appear.
It could
If a knock sensor was bad, the check engine light would be illuminated and the code(s) set would indicate so.
Engine coolant temp sensor. I would check codes if you have a ECT code replace the sensor. does the check engine light come on with key on engine off, If it doesn't replace bulb. If the engine light works check fuel preasure,
The check engine light would illuminate and the code(s) set would lead you to which O2 sensor is at fault or why the sensor set the code.