I tend to agree with dpollitt, the images don´t really look soft.
Recently I´ve started shooting with the D7000 and it appears to be somewhat unforgiving at areas that are not exactly at the chosen focus point. Looking at the photos I would indeed expect a larger depth of field as well as a wider focal plane, especially the one shot at f/16.
Also I think you should take into account that AF Fine tune is easier with primes than with zoom lenses. With my 70-200 Sigma I did fine tuning at different distances and focal lengths to get an overall idea of where the combination of body and lens performs best and find an average. It is not uncommon to experience a bit of a focus shift when zooming in/out.
I don´t know what camera you were using before the D7000, but I have noticed - comparing it with my D3100 - it takes some time to learn to work with the larger amount of measuring/focusing options. For instance the custom setting b4 (size of the center weighted area) can have a remarkable impact.
As a sidenote, I think you should really try shooting RAW to make sure the camera does as less compression as possible. Make use of the captured data; in post processing you´ll simply have more information to work with.
Hope this helps!