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
GASOLINE ENGINE OR DIESEL?
you have a stuck valve
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.
There are quite a few relays and solenoids that are activated when an engine is turned on. Some of them make noise.
The A/C system compressor operates when in the defrost mode. If the noise is also heard when running the A?C it is more than likely a problem with the compressor/pulley.