I no longer play games on my iDevices -- not even my beloved chess -- there's just not enough time.
So I can't oblige you regarding games
. As johhnyb explained, if a particular iPhone game has already been upgraded for iPhone 4's Retina screen
(which it definitely should have, by 2013!), then it will appear crystal-clear on an iPad 3 or iPad 4 screen.
As to the "2x" button, that's easy. It will automatically appear at the bottom right corner of your iPad screen, as soon as you open an iPhone-only app on an iPad. So, you press that "2x" button, and the iPhone app will fill out almost the entire iPad screen. You can see it in my screenshot I have just posted above. (In my screenshot, you can see the "1x" button -- pressing that, the iPhone app would display in its original iPhone resolution, leaving most of the iPad's screen empty.)