[..] I always depend on AF or the focus aid in the optical viewfinder. And thus I always use the 4-way switch to move the single AF point around.
Sometimes I feel pressed, because I cannot move the AF point, and the 4-way switch doesn't respond. Then I find that the "L" lever around the switch is inadvertently set to "L" position, which happens every one in a while.
My usage with the D600 is very similar. I mostly use manual focus lenses and use the matte focus screen as much as possible, but often end up having to move the AF point around and use the "green dot" focus confirmation. It's not an ideal solution but can help when lighting conditions are poor and accurate focusing using the matte screen is not possible. Even then I am not always convinced it is entirely accurate. I recently took some pictures in a forest with my AIS 35/1.4 at f/2.8. Lighting was dim and even after multiple attempts using the green dot I am not sure I nailed the focus. Maybe my lens is not sharp? I should have tried live view but that's tricky when shooting hand-held from a swing-bridge. Maybe time to buy an AF lens
As for which eye to use, I am right-eye dominant, but my left eye sees a little more clearly so I often focus and compose using the right eye, and do a quick check with the left before taking the picture. So far I have not locked the AF point by accident, but it is a useful reminder if it ever happens.