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If I connect my Note to my computer, can I move multiple files from my Dropbox to my Note, instead of having to export them one by one via my Note app?
You should be able to do so. I have moved pictures back and forth before like the phone was another drive. It isn't something I have done often with many of my phones.
What is probably easier is to get the Dropbox app on your phone and log in, anything in Dropbox would be available to your phone and computer.
Yes. You can use it as a mass storage device and move files back and forth from phone to computer and vice versa. Any files... Movies, pictures, music, docs, etc.
But remember.. Dropbox, Google Drive, One Drive, etc.. All have mobile/tablet apps. Things can be set to auto sync and you only download a file if you need it. It is available to look at from phone and computer Less work than hooking your phone up and copying files that you can easily download with an app to your phone.