Apple don't provide any official APIs for doing what you ask.
Unofficially, you can try the stuff here: https://bitbucket.org/tristero/ipodaccessframework
You can definitely use it to determine whether a particular app is installed (by looking for a match for its bundle-id) and you can read/write files to/fro a particular apps document directory.
Disclaimer: this one is mine. There are definitely other libraries around that achieve similar results.