Yes, if you want to use both IPs at the same time. It is up to you on if you want to provide external IPs to your internal interfaces, but it is not needed. The key is that the internal interface(s) have access to the LAN data, regardless of the IP scheme used on it (which is why many do use the internal LAN network IPs).
Yes you will need to setup a VIP on the internal interface.
The IPs can be private IPs as they will connect only to your network.
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