There are pages and pages and items that can cause a check engine light. You need to have it checked for codes with a scan tool. After repair light can be shut off with scan tool.
Alternator straining to maintain battery charge?
It is probably your cooling fans. These are electric and may run with the engine turned off. It is probably your cooling fans. These are electric and may run with the engine turned off.
when stopped at red light or when in park
you have a stuck valve
GASOLINE ENGINE OR DIESEL?
Bring to a shop and have it scanned to determine problem
In order to tell you that you would have to describe the noise and what the car is doing when the noise is made. Are you idling, driving, just turned the AC on? What is occurring and what is the noise? Idling and sounds worse when AC is on. Sounds like it is coming from the top of the engine. Vehicle has 120k miles
The frist thing I would check would be the engine mounts.
There may be some drag on the AC clutch when it is disengaged as the clutch 'free-wheels' during this time. When you engage the AC ,the clutch 'locks up' and the noise disappears. If the noise gets worse you may need to replace the clutch, if it stays the same and it not very loud, I would not replace it.
Your transmission fluid might be low.
Not likely. A bad O2 sensor would illuminate the check engine light and the engine performance would suffer.
Noise. Without noise, it can't work. Noise is in an engine, and without it does not work. Every engine has to make some kind of noise, internal or external, inside or outside the engine.