A point was made that none of the pictures have a point as sharp as it should be. That's interesting. I don't know that but it seems as sharp as my 50 1.8. More or less
That could be due to being unprocessed and posted here (web compression, etc).
Something doesn't make sense...
The camera's PDAF system compares multiple separate images (aperture dependent) taken from the objective lens, and it determines if the images are "the same" (in phase). If they are, then the camera believes the image is in focus. There is a tolerance built into it so "in focus" may not be maximum/critical focus, and AFMA allows for fine tuning. This is all fairly lens independent in that PDAF can work w/o any electronic/data communication w/ the lens.
I've never seen PDAF that far off, I'm fairly certain it is well beyond the AFMA range. Additionally, it should not be "worse" when the subject is farther away and there is more DOF. However, it is quite possible for the camera to be set/operated so that it will take a picture w/o achieving/confirming focus... if the lens is bad, this is the only thing I can think of that would allow this. And it is quite possible for the camera to be focused at a point other than where you think it is (technique/settings). In all of the example images the point of focus seems to be somewhere closer to the central AF point rather than where you want it (actually appears to be low center).
Have you confirmed that the camera is reporting the correct point of focus and that it believed the image was in focus? Have you tried/ensured that the camera is set to use only one focus point (center), only focus once, and will not take a picture unless it's in focus? Without doing those two things we cannot rule out technique/camera settings as being the cause.
As I said initially, it is not uncommon for an older wide aperture film lens to need AFMA. You could try that w/ the D7000; I would just set it to the max (-20) and see if/how much that helps. But if it's some other setting/technique, this will just confuse the issue.