Although I think you know what you are doing, your explanation is really bad!
for this i'm assuming the camera is in spot metering, which means that it will measure the amount of light coming from exactly one spot (the center) of the camera's view.
This isn't true. With spot metering, the camera will only measure a very small area of the scene - normally around 1% - 9% of the frame. Not a "single spot"
In-camera metering is standardized based on the luminance of light which would be reflected from an object appearing as middle gray. If the camera is aimed directly at any object lighter or darker than middle gray, the camera's light meter will incorrectly calculate under or over-exposure, respectively.
Then if you are in manual mode, it will show you how much light is getting to your sensor, for your selected aperture and shutter speed. Furthermore it will tell you how much light is getting to your shutter by comparing it to a 'normal' exposure for your chosen ISO.
Manual, Semi Auto and P all show your exposure meter
An in-camera light meter can work surprisingly well if object reflectance is sufficiently diverse throughout the photo. In other words, if there is an even spread varying from dark to light objects, then the average reflectance will remain roughly middle gray. Unfortunately, some scenes may have a significant imbalance in subject reflectivity, such as a photo of a white dove in the snow, or of a black dog sitting on a pile of charcoal.
Selected aperture, shutter speed and ISO together make your exposure and contribute to correcting your camera's inability to make accurate decisions.
So if the meter reads 0, then that particular grey spot is shining exactly enough light for a perfect exposure.
That's not the case at all. What if there are no grey spots?
When the camera meter is centred your scene (or part of a scene of using centre weighted or spot metering) is reflecting light back that would be measured (averaged) as a middle grey.
IF the meter reads -2, then you are getting 2 stops less light than a perfect exposure for that area, and you need a slower shutter speed, or wider aperture etc.
Not necessarily. A perfect exposure may require a -2 exposure compensation. A perfect exposure can be many things depending on what you want from the scene.
If you are shooting a standard subject then yes it is likely that your shutter speed, aperture OR ISO is wrong and you can amend any of the three to correct the under exposure.
However, the problem is that scenes do not always have the same amount of illumination. So if you metered on a relatively darker patch in the middle of a lot of really bright areas that weren't in the area you metered, then the bright areas will become over exposed, because you set the camera to have 'proper exposure' for the darker areas.
I see what you are saying although it would be difficult for a newbie to understand.
Now, what is meant by recomposing, is that you often choose to meter off of a particular subject. Bryan peterson likes to meter off the sky a lot for example, because he has found that it seems to be reliably close to the 18% grey that the camera already assumes it is. But since you had to chose a particular place to meter, the picture may not be the composition you desired, you may have wanted to take a picture of a person on the ground, but needed to meter off the sky. So after metering, you reposition the camera (recompose the shot) and take the picture using the settings found while metering off of a more reliable (ie, the sky) area of the scene.
I see again what you are trying to say but it reads as gobbledygook....
Metering off the sky is NOT always ideal because generally it is much brighter than the ground. A sky is certainly not generally a middle grey. f it was then we would all meter for the sky and be happy
Generally if you set your camera meter to expose the sky correctly, your subject on the ground will be badly under exposed (without flash to expose your subject). Bryan only uses metering from the sky in very specific circumstances for a particular image.
Your example of recompose is verhy difficult to follow - last sentence would have been enough.
Not meaning to be cheecky but you need to be sure what you are writing is correct.
There are many websites with great info and probably better to redirect them. I know you have the understandingthere - just the explanation doesn't read very well and there's a little inconsistency there.
Regards
JD