There are no private messages between users on the SE network.
If a user has recently been present on chat, you can ping them there. If you have enough rep you can start your own chat rooms, and even limit who can speak in them.
If you want to speak to a moderator privately, they can set up private chat rooms which only you and them can enter. You can ask for this in chat or via a flag.
Moderators do not see deleted comments without specifically asking to see them. If you want to leave a note for a moderator but don't want others to see it, you can leave a comment, delete it, and then leave another comment asking the moderator to see the deleted comments. In general if you choose an old post of the mod's to comment on, the chances of anyone else coming across it before the moderator sees it are slim.