I don't know exactly what your diagram said,
and I am far from an expert in m0n0wall,
but I have 2 m0n0's up, so I'll give you my 1 cent...
For simple access from LAN to WAN and from DMZ to WAN,
you should not need NAT - unless that is to meet some
other addressing requirement.
By default, m0n0wall has a default route set for the WAN.
Also by default, there is a rule for Allow All traffic from LAN to WAN,
because the LAN is presumed to be in your control.
If you want to replicate that on the DMZ, you can
go to the Firewall/Rules screen and click the + symbol
next to the rule. If you change nothing, it means duplicate exactly.
If you change just the Interface and Source Network - and the COMMENT,
you should be in good shape.
Do you want to post more info, eg, a cut/paste from
the Rules screen, a screen print (crude), or a config.
Or mail privately...keep encrypted passwords to yourself.
Maybe someone else can elaborate on how outbound traffic
works...I know that my traffic goes on the internet using
the router's WAN IP address.