I'd love to find a way to securely share passwords with mobile devices. But from what I understand, there's no very secure way to do it on Android. If you store a private key on the device then other applications may have access to it. And with iOS, each app is its own silo, so I'm not sure how you'd get password autocomplete working. An ideal solution would allow selective sharing because there are some secrets you wouldn't want stored on your mobile device.
Applications are separated by Linux permissions on android. Attempting to read or write to other application directories simply won't work. Your fear is not correct for the average case user
It depends on how you do it. If you use the local app storage, it's protected via the OS. Only the App itself can read/write from it.
If you use "USB Storage" then the data is stored on the sd card or equivalent. Any other app with the USB Storage permission can read or write to that directory and it's very much not secured.
As for interfacing with other apps to "autocomplete" your password, there are permissions and ways to do that too, although I can't speak for them since I've never done it.
