yes
It will usually come on. The speed sensor on my transmission died and it displayed the check engine light.
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.
The oxygen sensor is one of many things that could turn the check engine light on.The oxygen sensor is one of many things that could turn the check engine light on.
Yes
yes
it is probably throwing off a sensor, like the mass airflow or map sensor and causing the check engine light to come on
If it is bad the check engine light will come on and set a code for that particular sensor.
Yes, it is one of many things that can cause the check engine light to come on.
yes
Check engine light will come on for various reasons. The o2 sensors could be one of them. If your belt breaks the light will come on and the engine will over heat. I mentioned the o2 sensor because when it comes on for this reason some people have had that light on for years without replacing the sensor.
Yes, that is one of hundreds of possibilities for the check engine light.
Every sensor on the engine and transmission can cause the light to come on.