The f/number is theoretical*. Strictly speaking it only applies at infinity focus and for exposure it assumes that the lens elements are perfectly clear. In practical terms, that's close enough with most lenses, most of the time - unless you have say a zoom lens rammed with glass or are very close to the subject. At macro distances, with a magnification of 1:2 the effective aperture will reduce one stop, and two stops at 1:1. The f/number always holds good for depth-of-field calculations regardless.
Vignetting is an optical fact of life and even the most expensive lenses suffer from it, commonly getting one or two stops darker in the corners at maximum aperture. Fast lenses like f/1.4 and wide-angles are worst affected, but vignetting always reduces dramatically as the f/number rises. By f/4 it's usually hardly noticeable and pretty much invisible from f/5.6.
There is another form of 'vignetting' that happens at the sensor when pixels around the edges are unable to capture all the light coming from oblique angles when the lens is very close to it, eg wide-angles. Mirrorless cameras with their shorter back-focus distance make this worse.
Most of the time, all this passes unnoticed. While Nikon cameras report the changes with macro correctly, Canons simply ignore it to prevent confusion. Either way, TTL metering accounts for any changes automatically and of course the histogram/blinkies show what's actually going on at the sensor.
For movies, when the same scene may be shot from different cameras/lenses simultaneously and then edited together, even minor variables can be a problem for consistency so they're usually marked with T/stops that are adjusted for actual light Transmission rather than f/numbers. These days, exposure aids like the histogram plus blinkies and zebras make things a lot easier.
*The f/number is simply the focal length divided by the diameter of the entrance pupil, which is not the same as the diameter of the front element.
