So, it is not a security thing, as those apps are signed for use. By default, iOS and iPad apps are available for download, UNLESS a developer ops out, like some very mainstream apps. But, the fact it is there, doesn't mean it will work.
What is odd is that you have tried them all, and none work. I'd contact Apple. I searched the Apple Support forums and there is nothing on this at all, so it doesn't appear to be a widespread problem.