The files metadata.db and metadata_db_prefs_backup.json should not be on your tablet. They are the calibre database files.
I have no idea why Moon+ is not installing on your tablet so that it "advertises" what kind of books it can read. I use Moon+ pro on all my devices (Nexux 7, HTC Sensation, Galaxy Nexus, Galaxy Tab 10.1) and it works perfectly. The only thing I can suggest is the "nuclear" option: reset the device to factory settings and start over.
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