Using Hazel for automated backups

I'm looking to automate some backups to an external drive. Does this sound like something Hazel can do?

When I plug in a certain external drive, copy everything from a specified folder to that drive (skipping any files that have been copied previously), and (this might be the tricky bit) notify me of any files which have been deleted from that folder but were previously copied on the external drive.

The notification of deleted files is going to be problematic. You can use the sync action but it doesn't have any way of notifying you of deleted files. You'd have to use a script or some other software specifically geared towards this type of thing.