Is there a way to control app execution environment? Is there some way of controlling how an installed application communicates over the network and writes data to disk?

Let's say I have an application that will handle sensitive data, but it comes from a third party so I can't control the implementation. Is it possible to provide some kind of environment where I can run the app and make sure that the data it writes to disk is encrypted and that its communication over the internet is secure? Like running it in a virtual machine that I control or forcing it to use some kind of framework I've created?
The Android Emulator can be run on your PC and is good for testing.  You could use tools to sniff the data being sent on your network and see if it's encrypted, and check files written to the "device" storage.  But you can't "control" the app per se.