Looks like it is solved. First of all, instead of "localhost", I put the hostname of the machine.
Secondly, I put the user rule after the group rule
%wheel ALL=(ALL) ALL
<my_username> <hostname> = (root) NOPASSWD: MOUNT, SHUTDOWN
and it seems that did the trick. Now I can mount/unmount and shutdown without a password and for any other sudo operation I am asked for a password.
Thanks for the replies.