Are you saying there is green around the edges of your image frame when you key out the green screen?
If so, what you want to do is use a Garbage Matte. My favorite for this is SliceX from CoreMelt, but the cropping and Matte effect built-in to FCP X work great. You want to mask out all the "garbage" that you don't want to deal with.
As for making it sharper, There's not a ton you can do to sharpen up video, as you're shooting interlaced.