The close-up of the hawk is VERY sharp, in the eye. The shallow DOF is what's killing the feather detail on the side of the head. I generally don't go beyond f/11 and the sweet spot of most telephoto lenses is usually around f/8. I shoot Canon, but I'll bet that camera will produce great detail up to ISO 1600. Be careful with luminescence NR, it'll kill detail. I lower the level and put up with a little grain in the background.
The flying hawk actually looks okay, but it's a real odd pose. It's back lit and I suspect that you had to crop it quite a bit.
Shoot lots and lots of shots. I find poses that I like and then reject anything that doesn't have a super-sharp eye. For BIF, pay attention to where your AF is hitting. I'm always disappointed that I don't get more right on the eye. I miss the whole bird a bunch, but the AF system can be amazingly forgiving if you've put the AF point on the bird for part of the time and you're using Servo Mode (I think Nikon calls it Tracking).
Lenses do make a difference in this league. Start saving for a prime 300mm or 400mm. The top Nikon shooters that I work with use the 300mm and 600mm primes. Still, I see some decent shots from the Tamron 150-600mm. All these lenses demand practice and paying attention to technical details. Stick with hand holding and you'll get better and better. Plan to shoot hundreds of shots every outing. If you have a subject cooperating, keep milking it until it moves on.
Here's one of 50!! Damn bird never did anything interesting, but I was nice and close, with a 700mm setup on a crop sensor camera. f/8 and be there:
Meadowlark Posing by
David Stephens, on Flickr