I think you are letting different uses of the words auto and manual confuse you.

• In the case of the AF/M switch on your lens, they refer to Auto or manual focusing. When using auto focus, the camera uses the point(s) you have selected to focus on what it thinks you want and focuses the lens for you. When using auto focus, you can select anywhere between a single focus point (that you, confusingly, can manually select as the auto focus point) and all of the focus points. How many focus points are available and in what groupings vary from model to model. When using manual focus, you set the focus by turning the focus ring on the lens. Some cameras will give a focus confirmation light or beep when you have manually focused on the items at the selected focus points, but the camera will not move the focusing mechanisms of the lens - you have to move them via the focus ring. Some, but not all, lenses will allow you to turn the focusing collar to fine tune the focus even when AF is selected on the AF/M switch. Be sure your lens allows full time manual focus before trying this, as doing it with lenses not designed to allow it can damage the focusing mechanism of the lens.

• When shooting in Av mode, you are shooting in an automatic exposure mode. It has nothing to do with focus. Av stands for Aperture value. You select the aperture setting you desire and the camera meters the amount of light in the scene and automatically computes the exposure and sets the appropriate shutter speed (or Tv for Time value). The M mode, or manual exposure mode, allows you to set both the aperture value and shutter speed, but if you select improper settings for your scene the photo will be over or under exposed.

Please note that you can use either auto or manual focus when using the Av exposure mode, and you can also use either auto or manual focus when using the M exposure mode.

Although modern focus systems allow you to choose from several points to tell the camera what spot or area you want the camera to focus on, this has not always been the case. Early AF systems only had one or sometimes three points. Before then manual only focus systems usually provided the greatest focusing detail in the center of the frame. When shooting a subject not centered in the frame, a photographer would often center the subject behind the focusing prisms in the middle of the viewfinder, focus the subject, and then recompose to shoot the picture. The danger with focusing and then recomposing is that the subject distance to the lens' entrance pupil may change slightly and result in slightly missed focusing, especially when using wide apertures that result in narrow depth of field. Knowing which way and how much to move the focus ring to compensate in such a situation was a valuable skill gained by practice and experience.