For crypto/security people on this thread, what encryption could app developers use to wrap their API call so that the least amount of information is leaked to

For crypto/security people on this thread, what encryption could app developers use to wrap their API call so that the least amount of information is leaked to this kind of man-in-the-middle services? I.e, is it possible to: 1) hide which apps are installed on iOS/Android; 2) hide or obfuscate how frequently the app is used; 3) hide specific API calls I assume at least #3 should be achievable with additional encryption.