These are very interesting photos and do show a couple of things.
The open wings photo is degraded considerably by the high ISO 3200 noise. The D5200 is a very high resolution DX camera that doesn't have good noise performance at 3200.
The hawk lunch photo looks to be degraded by possibly diffraction. The photo was shot at f32 as reported by PhotoShop. You should try to keep the aperture below f11 for the sharpest photos. The same could be said of the in field photo but to a lesser extent at f20.
The first photo with the flying birds looks sharp enough, just a bit noisy at this enlargement for ISO 2000. With all my DX cameras I try to stay at ISO 1600 as a max.
I think the dove photo is fine. I'm just not sure where the focus point is, doves or branches.
Just remember this high a resolution camera will show up any errors much more than other, lower resolution cameras and especially at the longer focal lengths.