We'll create fresh WordPress site with Zippem installed. You have 20 minutes to test the plugin after that site we'll be deleted.
Zippem zips a folder on your site and lets you download it: your media library complete with folder structure; theme files which you’ve edited; plugins folder; or simply all files on your site.
By default, the target zip file is created under the uploads directory. There is also an option to delete the created file.
For upload and extraction of zip files, try: WP Easy Uploader.