A couple questions

I have a couple questions regarding admin functionality of the Zimbra
Network Edition.

- Is it possible to disable the "View Mail" feature in the admin
console? I don't want e-mail admins to be able to login to any user
accounts.
- If I were to do a backup/restore on a single mailbox, would that
person's custom settings (along with calendar and contacts) be restored
as well?

Welcome to the forums,

If you're a Network Edition customer domain level administrators can't view mail.

More advanced options: Bug 11515 - role based delegate administration

We will have a few admins that need full rights (domain admins are too limited), but we do not want them to have access to people's emails.

That is unfortunate...