Single focus point means that the camera focuses on that point at which it is selected. Auto means that the camera will automatically select which point it thinks it needs.
Think of focusing as a parallel transparent wall. If that point is in focus, everything on that plane will also be in focus from the center to the edges (within the limits of the lens capability at least).
So in your scenerao, if three people were standing side-by-side and you focused on the center one, all three would be in focus as long as they were on that same parallel plane.
And as you suggested, if someone is in front of, or in back of, stopping down your aperture will INCREASE the depth-of-field, resulting in the person(s) in front of or in back of being in focus (if you stopped down far enough and increased the DoF enough).
When I bought my Nikon 80-200 f/2.8, I was initially getting a lot of close-up photos that were blurry. Of course this was my fault, and I discovered that the reason was I had my focus set on Auto, and the camera would sometimes pick the wrong focus point.
I had to re-learn how to use the camera and went to Single focus with that lens so that I could select what was to be in focus. Problem solved. At open apertures such as f/2.8, the DoF is very shallow.
Although I had other fast lenses before the f/2.8 telephoto, the DoF becomes even shallower as the focal length is increased and the subject remains close. And the other fast lenses I had were shorter focal lengths so I never had the DoF issue.
So even though I had years of experience, I had to relearn a few things as I went to more capable lenses.
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