Hi,
To audit the deletion of the files or folders, the event 4663 should be the one we are going to check no matter for a file or a folder deletion since the event include all the information you needed. Such as:
who access the files or folders
information of the object type: files or folders
Process name: for example, explore.exe
Accesses: Delete
4663(S): An attempt was made to access an object.
Event 4660 should also be logged, but there is no object type information.
Event 4659 should be logged whenever user install a patch that requires replacement of a file that is already opened by Windows and can't be closed until shut down.
I also did a test in my lab to audit the deletion operation.
We enable the audit policy for Object Access,
Enable the folder audit:
When we delete a file or folder, event 4663 was logged.