What is the unit used for star brightness due to skyglow? What is the name and unit of the quantity in which star brightness due to skyglow is measured? How can it be measured from RAW image files of stars?
The brightness of a diffuse area is it's luminance, and can be quoted in units of $cd\,m^{-2}$. Measuring it would require knowledge of the properties of the camera: the sensitivity (at various wavelengths) of the ccd, the aperture, length of exposure and so on. This could probably be found using calibration images, in which a known luminance is imaged and then the brightness of the skyglow is compared.

The brightness of a star is usually given as a magnitude which is related to the amount of electromagnetic energy received from the star per second, in a particular range of wavelengths.

It's unclear what you mean by "brightness due to skyglow". The brightness of stars is not due to skyglow, but excessive skyglow can mask dimmer stars and diffuse objects.