Google-drive – How to read epubs stored in Google drive on mobile phone

Google itself does not provide any such facility. Anyhow, what you are asking is completely possible by using ifttt.com.

I know that Google Drive has a "Copy to My Drive" option when you right click on a file someone shared with you but I don't think that can be done automatically from within the Drive webapp.

There exists a Drive API however that I think can easily be used in a Google Apps Script. I have no experience with Google Apps Script, but a little googling brought me to this question on StackOverflow.

It appears to be fairly easy to manage Drive files from an App Script. I'm not sure if you can make Google Apps Scripts to do automation (like continuously checking Drive for new files), but I think it should, go and find out for yourself. If it can't do automation, you could launch it every time you discover new files in the shared folder.