visibility / password failures

I have almost all pages on one of my sites password protected,
under ‘visibility’ on one of my sites. Is there a log file where I
can see whether or not visitors are entering the correct password?
I could derive from stats by the length of visits, but I’d like to be sure.
Also – can I use more than one password on a page – without having to define a user? (Password for visibility either password-A or password-B)

Thanks in advance!