Can Android extract zip files? If so, could you please explain the process of downloading and extracting a zip file?
Yes, provided you've got an application to deal with zip files, you should be just fine:
By default there's already apps within your OS to deal with zip files:
Best is access a zip file thru your browser, download an open one. A window should pop-up, with some recommended apps already on your system.
Android allows downloading of any file type irregardless of size (FAT32 formatted SD cards however allow only up to 4GB per file).
Many file explorers come with built-in ZIP support -- and again, many also offer access to network ressources via FTP, SFTP, FTPS, Samba (Windows Network), and more. Some good examples for these include:
Of course they offer a wide range of additional features.
Downloading then either takes place using the file managers network capabilities to browse the resources and copy the file (as you are probably used to with file managers on your computer; on Windows, Total Commander is already widely known and used) -- or, alternatively, using the web-browser, which then stores the file on disk. Once on the local file system, the mentioned file managers offer you to open/extract the archives (a zip file is an archive) either when directly tapping on the file, or via its context menu (usually opened on tap-and-hold the file entry).
Should be pretty easy and self-explaining -- though some of the file managers also offer tutorials / online help / inline help to guide you: