Hi Chris! Did you have a look in your user prefs? That’s where you can determine whether or not you get sent emails when notified.
“Privacy” of personal messaging has been discussed at length here - you might try using the search. Like with any system, I don’t think users expect that admins cannot see their messages… if they do then they are sorely mistaken. The only way to do that is with encryption keys, which I think is available as a plugin -Discourse Encrypt - RFC - though I’ve not tried it.
Here on meta there are lots of admins who can see everything… in my community it’s only one person. Moderators do not see personal messages except their own.