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Joanna - you can relocate the configuration folder used by the 'installed' versions of calibre via CALIBRE_CONFIG_DIRECTORY environment variable - see
Customizing calibre.
Whilst it is not officially recommended/supported, some calibre users keep there libraries etc on Dropbox; notably DoctorOhh, a long time user (pioneer) of calibre, and an MR Moderator. I suggest you send him a PM and canvass his thoughts.
BR