There should be several Chess alternatives that will work cross platform. You will probably have to do some research to pick the right app and host. I see there is a Chess for FaceBook app. I'm guessing Android will have one too.
You will not be able to FaceTime; however Skype will work on both the iPad and Android devices. Like FaceTime, Skype will allow you to video chat.
On the other hand, you can forget you heard that if you want to keep the pressure on for an iPad 3.
P.S. Did a little research after the fact. Chess.com has apps for both Android and iOS phones. While an iPhone app won't look as nice on the iPad, it will probably work. That is probably also true for the Android phone app on the Nexus 7, though not quite as bad since their isn't as big a size difference.