Kindle

Local State Storage

/Users/<username>/Library/Containers/com.amazon.Kindle/Data/Library/Application Support/Kindle/My Kindle Content

Deregister a Device from Kindle

Kindle → Preferences → General → Deregister.

"Lost" Collections on iPad

The collections are probably not lost, it's just that the app was inadvertently reconfigured to display then in a different "View" ("Grid", "List", not "Collections")

Library → Sort ⇅ → View → Check "Collections".