I have a 7D, and I'm with Michi, that a 3+ underexposure will bring out all that chroma noise and banding, which is the main issue with the second shot. (Chroma noise is the colored noise, while luminance noise is the black/white splotchy.) I bet that one was pretty dang dark out of the camera!
You miiiiight be able to limit the chroma noise in shot 2 a bit by doing this in Lightroom: (I actually only have Lightroom 3, so not sure if LR4 is set up the same..).
Under Develop, scroll down to the "Detail" section, and in there is the Noise Reduction section.. Then bump up "Color" from 25 (default) to around 35-40.. It miIIiight dull your colors just a tadd, so them bump your contrast a couple notches and your vibrance.. It should bring the image back pretty well, without all that chroma noise.
As for your first shot, I don't have much experience with nice blue sky pictures.. That looks like a lot of noise, though. Also, how much did you crop that shot? It looks like it's pretty close to a 100%, so you pretty much max-cropped? That would be my guess, anyway.. If that's the case, there's not much you can do besides getting a bigger lens.. The hawk doesn't look that bad, really, just a bit tiny!
You can also try messing with the Luminance noise reduction in the hawk shot, and then do sharpening, though.. And if you hold down Option/Alt (on an Apple at least.. not sure if it's the same button on Windows..) you can see the "sharpening mask" as you adjust it, which essentially defines the sharpening edges.. It'll let you not sharpen the noise, while still sharpening the hawk. (Hold down option, and then click and drag the "Masking" bar under Sharpening, which is juuust above the Noise Reduction, you'll need for your second shot.).
As for a bigger lens, you're kinda limited..
You've got a 400 5.6, which doesn't really allow you to add an extender, because you lose autofocus..
You can get a 300 2.8, which will let you do a 1.4x extender which gets you 420 f/4 (about the same as your 400 5.6, so no real advantage there..), or a 2x extender getting you 600 f/5.6. Howeverrr, with a 2x extender, you really need to stop down another couple stops to get back to a crisp image.. so you're looking at not shooting faster than f/8 to f/11, which cann be limiting...
A 400 f/4 is sort of non-existant, except for the DO, which is crazy expensive..
Then there's the 500 f/4, 400 f/2.8, and 600 f/4... And they're all crazy expensive. And bigggg and heavy. And really, neither 500 or 600 give you a HUGE increase over 400mm.. BUT, they both offer you the ability to throw a 1.4x extender on them, which does help get that extra reach.
Also, if you were to upgrade to a 1dmk4, you lose a bit of the crop, so your 400mm doesn't reach as far, which will them make you bang your head into the wall even more, haha. : D Really, it's just a bigger lens you need..
Aaaand lastly, in my experience, the 7D is just kinda noisy.. But I really don't have a problem with it. And I would say it's consistently noisy from ISO 400 til ISO 1600.. I don't notice much of a difference. After that, though, contrast definitely falls off, and detail starts going, but I use ISO 3200 nooo problem! But definitely not if I'm doing a big crop. And definitely I have no problem using it if I have substantial light.. Once you start pulling exposure, the higher ISOs are much more noticeable.