Here's my test results with the 80-200 AF-S @ f/2.8 on a D7000. The image is full-frame, but has been resized to 1600px on the long edge during export from Lightroom.
Note how the chart is aligned almost exactly with the frame, and the chart fills the frame? The angle has also been measured to as close to 45ΒΊ as I could manage.
Before returning another camera, try to replicate these test conditions and see what the results look like.
Also, have you conducted tests with any other lenses?
In answer to your question about AF points, the AF methods are different between live view and when using the viewfinder.
With the viewfinder, phase detection AF is used. With Live View, contrast detection is used via the sensor as the mirror is up and the AF module can't see through the lens, so the same focus points can't be used.
You can see from the above chart that this lens very slightly backfocuses. With an adjustment of -3, here it is again: