I've had 3 app downloads since I downloaded iOS 7, but the apps still show up in the "updates" section of the app store with the "open" button present. Is this normal?
As has been previously discussed in a number of threads--this is the way it is now, and until/unless Apple changes that at some point (or there's a jailbreak perhaps), it is what it is.
Technically it is Purchase History. This is a feature that's part of the App Store Volume Purchase Program and Apple may not want it cleared. I'm expecting many changes in the months ahead and it won't surprise me if this feature is added.
As there is a separate tab at the top to select the full purchase history view though, my thoughts are that this should hold the full list and there should be an option to clear the default latest updates view as others are requesting.