Seeking Advice on Automating Archive Cleanup + Rename Rules

Several issues here.

First, understand that the Unarchive action already throws away the original archive after extraction. Any actions in the same rule operate on the extracted contents. If there are multiple files, they are put into a folder with the same name as the archive.

If you want to save the archive file, you will need to copy it first. Note that any actions in the same rule after a Copy action will act on the copy, not the original.

As a result of the above, you need separate rules. By default, Hazel only executes the first rule to match a file so you will need to use the Continue action to allow a file to match multiple rules.

I don't know what kind of renaming you are doing and what kind of contents are in the files. You will need to provide a lot more detail on that.