Does iTunes Backups Happen Automatically?

You need to set up iTunes to allow you to do the backup over WiFi and you need to sync the two devices at least once. After that you should be able to do it, provided;

  • Both devices must be on the same WiFi network
  • iTunes must be open on the Mac
  • The iOS device must be charging

No, there's no option in iTunes or Finder to make scheduled backups, they must be started manually (backup during sync is still a manual backup). If you want automatic local backups, you'll need a third-party iTunes replacer with that option.