No and no.  Automatic Updates will take care of all the Critical stuff, which is all that's essential.  You can still visit Windows Update and run manual scans to see if there are any new non-essential updates in which you might be interested, but that's optional.

You don't need to uninstall any updates unless they're causing a problem with something, which shouldn't ordinarily occur.

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@MarilynArnold wrote:

If I have the automatic updates checked and install them when I am prompted to do so, do I still have to go the the update page and download and install the critical updates from there too.

Also do I need to delete any old patches that are now installed that I no longer need.

No.

No.  Do NOT delete them.