Where are displayed shortcuts stored? Often after a reboot, crash or USB usage, icons of apps go missing.  Both in the "Home" screens and "Applications".

Currently I have four screens of apps, three in Home. Some of the icons understandably vanish when the SD is taken by eg. USB Storage to PC mode (because they are in part stored there), but often refuse to reappear even after restarting the phone.

Is there config file stored somewhere in my rooted Android 2.2 responsible for the current desktop layout of shortcuts?  Or way to back it up &amp; restore (even the stale shortcuts), or force refresh based on existing apps in internal or external memory?
App specific settings are usually stored in the internal storage folder accessible only to that app. While apps do have the ability to write to external storage and lose access to that data when you mount it, I doubt that is the case here.

When you install and move an app to the SD Card, you are not moving the entire app. Some core content of the app still stays on the internal storage. However, moving an app to the external storage has some interesting side effects. The app is completely disabled when you connect your device to the computer, on pre honeycomb devices. Android 3.0 onwards, the USB storage was switched to MTP, which allows the device and the computer to access the storage simultaneously.

In your case, when you connect to the computer, the apps on the SD Card are disabled, causing them to disappear temporarily. As for them not reappearing when you disconnect and restart your phone suggests that there is a bug in the launcher you're using. Try using a different third party launcher instead.