Hello Leigh, welcome to the Microsoft community, I'll be happy to help you today;
I understand that you are having issues with your printer and Windows Update;
Initially we need to solve the Windows Update problem try the following;
Completely uninstall any third-party antivirus you may have previously installed;
run the Windows Update troubleshooter;
Press Windows key + i and go to Update and Security;
Click Troubleshooting and then Additional Troubleshooting;
Select Windows Update and click Run the troubleshooter;
Stop Windows Update services;
Press Windows key + X and click PowerShell (Admin) to open PowerShell as administrator;
Copy and paste the commands below and press Enter after typing each command line:
net stop bits
net stop wuauserv
net stop msiserver
net stop cryptsvc
Remove Windows Update files;
Press the shortcut keys "Windows + R" and in the run box:%windir%\softwaredistribution\ press Enter;
Delete all content inside the softwaredistribution folder;
Restart Windows Update Services;
Press Windows key + X and click PowerShell (Admin) to open PowerShell as administrator;
Copy and paste the commands below and press Enter after typing each command line:
net start bits
net start wuauserv
net start msiserver
net start cryptsvc
Check if you can download updates now;
If the problem with Windows Update is resolved, let's try to solve the problem with the printer;
Uninstall any software you installed for the printer:
https://support.hp.com/us-en/document/ish_19800...
Then follow the step by step steps in the link below to install printer drivers and fix printing errors:
https://support.hp.com/us-en/drivers/selfservic...
Hope this helps, see you soon!