Can macOS system open zip and tar archives natively?
OS X can handle both by default from Finder. The Archive Utility that ships with OS X knows how to extract both formats. Just double click on the file or Cmd-Click (or right click) on the archive and select 'Open' from the list and OS X will unarchive it.

Users also have access to zip, unzip and tar from a Terminal window command line. These all come with OS X.

There's also the free, and most excellent, Unarchiver that they can install that allows for a few more options when dealing with compressed files. It also supports a few more formats. But it's completely unnecessary for extracting gzip-compressed tar archives and zip archives.