Nice set. It's hard to 'completely' freeze action like that @1/2500 so the first shot appears ok to me, although I believe a larger f/stop might've helped toward decreasing the ISO and lowering the noise a bit. I sense you did some moderate cropping. With them being @ 500 and 340 mm, cropping can make any noise stand out more. I struggle with processing pics like that all the time.
not sure if a faster shutter speed or faster af was needed in this situation since i can't see it larger. it looks like the af to me at this size. shooting the bird so that the head and body are on the same plane would keep it in focus.