I'm supposing that the app's personal information, for example SharedPreferences and SQLite databases, survive the phone's internal storage as opposed to the Sdcard, even when the application itself is a component of the Sdcard.

I can not look for a simple explicit confirmation of the anywhere. Can someone insert?

Yes, personal information live in internal storage. I have examined this by exploring file system on rooted device.

If application is "installed" on Sdcard, only APK file is saved on card in certain encoded form. Other application data have been in /data/data// folder.