Comment by brundolf

1. Yes

2. Yes

3. I doubt it

But regardless of 3, simply by using the App Store at all (similarly to any other App Store out there) you're already giving them more information than they get from these hashes (at least for the apps that come from the store). I know for a fact that they keep a record of which apps you've downloaded there, associated with your account, because they check for updates and let you re-download them. As does the Android store. As does the Windows store.