Figured I should ask, 'cause if anything goes wrong I should at least have answers...

On the company webserver (LAMP), all clients (websites) are set up with an identical username and group. A former employee was fond of doing everything as root, and I will often be logged in as a website's user and be unable to perform certain tasks because root is the group and owner of files and directories. For all of our website users, I can't seem to su.

Should I add all users to wheel group so that I can su as them when necessary?

Also, I've noticed that when there are problems with the user:group setup for a public_html directory, the fastest way to have error-free operation is to chown the directory recursively:

chown [user]:nobody public_html ./* -R

The floor is open for admonishment

Any suggestions are welcome and appreciated.

Try su - (su space dash). That SHOULD give both root permissions and root path. Just su gives you just root permissions but only the path of the user you are logged in as (usually limited).

All of the server-created (WHM-created) users get access denied to su:

Take a look at the permissions of su. I would suspect that for some reason (not a good one that I can think of) the permissions have been set so a user cannot use su. I would change that. It is far more secure logging on as a user and suing than logging on as root.