If I have multiple users who sign into ILLiad on one computer and I set up DEBUG logging, will I need to do it for each user on the computer?
No. You will not need to set up DEBUG logging for each username that signs in on the same computer once you set up Debug Logging. It will be turned on for all Users on the same computer. If you are on a different computer, then you would need to set up DEBUG logging on that computer as well.
Here is the link to the How do I enable Debug logging in the ILLiad Client? help article.