Good point on the focus modes. The first image posted at the top of the page was Manual Focus. I found that the AF-A mode was not very useful and avoid it.
I generally find that AF-C is my preferred choice, but if you are having problems with focus, AF-S with Focus priority is okay for stationary subjects. The camera will not fire unless focus is achieved. I agree with the suggestion of single point AF for perched subjects.
My guess is the biggest issue is simply the capability of the lens. These images all look high zoomed - to 50% or more. On the D7000 with the 18-200 lens at 200mm you are beyond the limit of the gear. The D7000 at 100% has essentially the same magnification as the D800 at 100% (1000 pixels across the frame).