Even if you choose a focus area mode that uses multiple focus points the camera can only use ONE of those points to set focus - it can't use all of them, because focus can only be in a single plane that is essentially always parallel to the plane of the image sensor in the camera.
Page 98 of the D600 User Manual shows that the photo in post #1 (the scene contains many fine details, or other subjects that are small or lack variation in brightness) is a situation when AF will not work very well. In which case you should manual focus the lens.
The photo in post #10 is the situation noted on page 98 where there is little or no contrast between the subject and the background.
I highly recommend a careful re-read of the entire D600 User Manual, because the manual also describes how to turn on Mirror Up.
D600 User Manual Index page 340 - Mirror up ................................ pages 6, 83, 88.
You might also want to note in the Specifications section page 328: Focus - Auto focus that of the 39 focus points 9 are cross-type sensors; the center 33 focus points are available at apertures slower than f/5.6 and faster than f/8, while the center 7 focus points are available at f/8.
Note too that it doesn't tell you nor show you which 9 focus points are the 9 cross type focus points. However O think it is safe to assume the center focus point is one of the nine and that one is surrounded by the other 8 cross-type focus points.
The little square you see in the viewfinder isn't the AF point. The actual focus points are small slits. The square just indicates that the focus point is somewhere in that square.
The 9 cross-type focus pints have a vertical and a horizontal slit +. the remaining 30 focus points are single slits. Some of the single slits will be horizontal --- so they can detect vertical contrast and some are vertical slits | so they can detect horizontal contrast.
It's hard to be a craftsman doing any type of craft that uses somewhat complex tools if you don't understand how your tools work.