FIRST: Not all books on the device (applies to many brands) can be added to Calibre. They may reside in protected (from user access) storage. Next, there is DRM. Calibre can STORE books with DRM, but they can only be used with devices that was registered with.
Next is KFX books: I can't answer the question of 'Will the KFX input plugin work with what I suggest next".
Connect you Kindle: Allow Calibre to settle (on device column will populate with what it knows).
Switch to Device View: Select books WITHOUT TICKS: right click Add To Library
search: inlibrary: false