Does Apple keep track of iOS app opening?
I just tested this using Apple’s built-in “Music” app on an iPhone 4 running iOS 5.1, using ngrep and tcpdump to monitor network activity. No connections to Apple servers are being made when opening an app on any iOS device.

As you mentioned, individual apps (e.g. Facebook) may keep track of data like this by pinging a server every time you open their app — but Apple does not do anything like this globally.