AF is done with the lens at it's widest or maximum aperture.
If the lens aperture is set for your photo at a smaller lens aperture the lens does not stop down to the smaller aperture until the shutter release is fully depressed.
That is why AF uses just 1/2 a press of the shutter release.
Many variable aperture zoom lenses (indicated like this: f/3.5-5.6) have a smaller f-stop when zoomed out.
Consequently when zoomed out to f/5.6 somewhat more light is needed for AF to work than if the lens is zoomed in to f/3.5.
As far as the "f/8 combined open aperture", they are referring to use of a tele-converter (TC) on a lens to extend it's effective focal length.
Use of a tele-converter on a lens changes the lens effective maximum aperture.
A 1.4x TC changes the effective max aperture by 1 stop. A max aperture of f/5.6 is changed by a 1.4x TC 1 stop to an effective max aperture of f/8. (f/5.6 x 1.4 = f/7.84 which gets rounded to f/8).
A 2x TC changes the effective max lens aperture by 2 stops. For example it changes f/5.6 to an effective max aperture of f/11, in which case AF rated for f/8 won't work.
FWIW - the Nikon D4 uses Nikon's 51 AF point Advanced 3500FX Multi-CAM auto focus module and not the lower grade 39 AF point Multi-CAM 4800 AF module that is in the D610.
Also note that when a Nikon DSLR (F-mount) lens is not on the camera the lens aperture is at it's smallest.
When the lens is put on the camera the lens aperture opens to it's maximum aperture. so it is ready to AF.
