Does an action (or actions) exist in Nintex Workflow to copy a file from Nintex SharePoint 2013 on-premise to a SharePoint online tenant which also has Nintex workflow online enabled?

No, but I would try to do that this way:

Thanks Tomasz, looks very complex!

I can see how the binary of the file is passed this way, how would you pass metadata using something similar?

I know... But at the moment nothing simpler comes to my mind. I mean - I would try to go that way. Imho it should work and do what you expect even though its complex.

On the other hand as long as you are on premises you can always ask a developer to write you your own, specialized and dedicated action for Nintex Workflow 2013, that will receive some params and uploads your file. But in the end this action will be just a prettier representation of what I wrote above

Back to the metadata - as that method allows only file contents to be passed in the request body, I'd hit with another web service call now to the list REST API to update the item you have just created and to set its library properties, ex.:

method: POST
body: { '__metadata': { 'type': 'SP.List' }, 'Description': 'My list description', 'Title': 'Test', 'OtherInternalName': 'OtherValue' }‍‍‍‍

Source: https://msdn.microsoft.com/en-us/library/office/dn292552.aspx#Anchor_2

One more thing - you don't need to start your logic from O365. Following steps to obtain FedAuth and rtFa cookies you will notice that the first step is to send "SAML Request" - you can do it from on premise workflow, providing your "onmicrosoft" login and password. So in the end you can simplify it a bit:

1. Use https://community.nintex.com/community/build-your-own/nintex-for-office-365/blog/2017/02/09/working-with-security-credentials-requestdigest-fedauth-rtfa to get the cookies for O365 tenant following steps from your on premise workflow;
2. Set action to call O365 library REST API as I wrote above so that it will upload your file;
3. Set action to call O365 library (list) REST API again to set created file metadata.

Done!

Regards,

Tomasz