You can also specify whether or not any list  or Library is listed on the Quick
Launch bar  in Internet Explorer by changing the checkbox in the General Settings
section of the Modify Settings and Columns.

Document Libraries have an event module that you can use to tap into (including
audit) the various activities of your users. These events are subsequent and
asynchronous. Lists, however, do not have this capability yet.

The reason that the deleted user  is not shown in alerts  is because alerts are
fired subsequent to the action  and the delete physically removed any record in
the database about the deletion. Your best bet is to only give delete authority
to a few trusted individuals.

You may also want to consider using versioning on your Document Libraries.