I have all my notes now stored on my iCloud but I also wish to copy and store them on my device. Can I do this?
Once on iCloud, any other device with access to iCloud can store these files locally.
For OS X, go to System Preferences, sign in, and check notes.
For Windows, download iCloud for Windows: https://support.apple.com/en-us/HT204283
For an iPhone, sign into your iCloud account, then in settings, be sure that Notes is checked.
This should keep you in sync, and each device will store the notes locally as well.