A normal lens makes pictures with perspective that feels natural. That is most of what people mean when they talk about the human eye. On a 35mm film camera or full frame digital that would be a 50mm arguably down to a 35mm. On an APS-C thats 35-27mm, on a medium format it’s around 80mm depending on film format. Outside of that and one will often look at a picture and notice the perspective imparted by the lens’s angle of view. Smartphone cameras with wide lenses have also generally moved this preference wider angle. People have peripheral vision and are constantly looking around, so it’s not really about what you can see, but how it looks. Print size, viewing distance, and the individual shot all play into how accurate this guideline is. Keep in mind that with a good enough lens and film/sensor one could get a shot at ultra wide and crop the exact image you would get all the way to super-telephoto.
As a side note, I have an Olympus OM1 that I used to shoot sports with using a 50mm f1.8 lens. That particular combination was an exact match for my vision. I could shoot vertical images with both eyes open, tracking action with my left eye and focus and compose through the lens in perfect stereo vision with my right eye. I’ve owned dozens of other cameras and no other systems did this, but it was great.
It’s twice the light. Useful for shutter speed and focus sensitivity. Focus speed and accuracy depend based on lenses in question. If you are shooting in daylight an f/4 will be plenty. At a well lit big event f/4 is plenty. As things get dark, fast action, and you are closer in(requiring higher shutter speeds to stop action of players) that’s where the f/2.8 may be needed. With digital, high speed ISOs are so good, that it often makes sense for the enthusiast to jump from 3200 to 6400 rather than spend another $1000 on a lens. If you are making a living with it as a primary lens, just buy the fast glass.