Setting up DNS; Internet and Intranet questions

I have a setup as follows:

1) ISP->pass-thru-DSL-router->firewall-appliance w/ NAT support
2) NAT->DNS(Internet)

Let's assume:
a) ISP provided static IP is: 111.111.111.1
b) Firewall allows access to DNS port 53
c) Intranet addresses are: 10.0.0.x

Q1: In setting up a DNS server for Internet,
    is it required that I setup mydomain.com
    zone for 111.111.111.x addresses or can I
    use 10.0.0.x addresses since NAT is involved?

    What I am trying to understand here, am I required
    to setup seperate DNS servers, one for Internet
    (for 111.111.111.x) and one for Intranet (for 10.0.0.x)?

The trouble that I am running into is that I am not able
to get reverse DNS to work even through I have PTR fields
defined but they are of 10.0.0.x addresses and I am not
seeing rDNS resolvers.

Thanks!
Dan

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