How do i fully delete an old account so that it stops asking for updates?
By the general term "app", you ostensibly mean App Store? And if you did delete his Apple ID, then it wouldn't ask for updates.

You can either use a third-party program to remove those apps, or first delete them from the applications directory, then from Application Support located at ~/Library/Application\ Support/. If you cannot find it, then go to Terminal, located in Applications/Utilities  and execute:

open ~/Library/Application\ Support/


Then you can just delete the folder under the name of that app
Then, simply logout of his Apple ID if you failed in deleting it, and login your Apple ID