It's probably the catalytic converter fan; not the a/c fan.
No. While in air conditioning mode, the air will assist in the dehumidification.
Could be your ac compressor is going or gone, probably gone.
Yes, it would not make sense to run the ac and dehumidify when also running the humidifier.
For most cars the air conditioning is powered by a belt from the engine and even if the car is only idling it will be running without any meaningful effect on the car's battery. For some hybrid drive cars the air conditioning is powered electrically, so that it can work even with the engine off. These will drain the car's battery some, but the air conditioning controller will automatically turn off the air conditioning before this becomes a problem then turn it back on as soon as the engine is automatically restarted when it is again needed to drive the car.
Only when you don't turn it on.
You should consider running the air conditioning when it's colder outside than inside if the humidity inside your home is high and the air conditioning can help to reduce it, or if you need to filter the air for better indoor air quality.
There are many reasons why an air conditioning compressor might not turn off. There is likely a wire that is not connected properly.
A manual air conditioning system is one where you can turn it off and on when you want and control the temperature at which it is set.
The lights may flicker when the air conditioning is running because the AC unit draws a lot of power when it turns on, causing a temporary drop in voltage that can affect the lights.
No.
It is normal for a vehicle, including the Honda Odyssey, to lose some power when the air conditioning is running. This is because there are more devices running off the operation of the serpentine belt. If the vehicle stalls or shuts off, it might be a problem with the alternator or the air conditioning unit.
Running ceiling fans with the air conditioning on lowers the feel of the air temp by about 4 degrees. So in reality if you turn your thermostat for the AC to compensate for 4 degrees than you are saving a little energy.