I think your pix look good. That first one shows that you were panning because the dog is sharp in focus but the background shows blurred motion, that's a good thing!

As for cutting off the feet...are you using the LCD screen or the viewfinder to take your pix? Sometimes the LCD screen can have a slight 'delay' between what's actually there and add to that the shutter delay and it can cause things like that.

GREAT second shot of the dog digging. Love that sand flying out behind him!