Help for SBS 2003 setup

I need advice on Small Business Server 2003 setup. Basically my company is
co-sharing another company's premises. I want to setup SBS 2003 independently
from their forest but need to use their internet linkage. So if my network
is 192.168.2.x into their network of 192.168.1.x, can my SBS 2003 not cause
problems with their DNS/DHCP since my domain name is different from theirs?
I'm putting a router/firewall between the two networks. Their IT manager
reported that their DNS server received a zone transfer request from
192.168.1.54, my PC's IP on their network, when I was experimenting with 2
ethernet cards, for a non-existent or non-authoritative zone since my domain
is not established in their DNS and they do not wish to establish it for
security reasons. Can I with the firewall/router isolate my DNS from their
DNS so that no communication occurs between networks? Also, will my Server
2003 start to communicate with their servers for replication, active
directory updates or such. Basically I like my SBS2003 to be totally
invisible to their network except for internet access through their gateway.
Will exchange 2003 cause problems too with their LDAP and other networks?