When the updates are automatically downloaded and installed, what directory is the updates saved?

they are not...well, not exactly.

An update consists of newer versions of existing files, and they will be installed to the proper folders (usually c:\windows and c:\windows\system32)


the OLD files are actually moved to a backup directory, with names like
$NtUninstallKB??????$ (?=some number)

This allows you to uninstall an update if something goes wrong

You can make a schedule to downloaded and installed as your plan. For example, every day sometime, every Monday.....Sunday.

Open resource manager to click 'tools' menu, click 'folder option' submenu, navigate to 'view', select 'show hidden files and folders',enter path c:\windows, you will see a few folder marked blue font. Those are the path placed the default windows update files.