1. You need to configure DNS cluster for that WHM ->Cluster/Remote Access
2. Yes - provided you cannot manipulate your db through cpanel ( this is still in testing phase for cpanel ) . change your db access setting and use the db server through the LAN NIC
3. there is a feature called secondaryMX ( /etc/secondarymx ). When a domain name is added to it as well as to the /etc/remotedomains , the cpanel server will receive the mails, when your primary mail server goes offline, and sends the mails to the primary one, when the server is back online . You cannot check mails from this cpanel server.