the guest, update runs and then after some period of time closes itself. .... neither of these install
The first update is to the Windows Defender anti-virus software.
If Windows Update is running correctly, the failure of the other update to install should NOT cause the update to Defender to fail.
Can you double-click the green-coloured "shield" icon for Defender (in the System Tray at the bottom of the screen) and manually force it to try to update. Is this successful?
Then, go back to Windows Update, and click on "Update History", to see the newest date on which KB2267602 was successfully installed, and the list of dates on which it was installed.
Then, do a "check for updates", to see if ONE (or TWO) updates are offered.
This might be corruption within the Windows Update app.
There is a Microsoft "troubleshooter" for issues with Windows Update. Run it, and see if it makes any changes.