Here's a thread in which Vel discusses the OCC (=One City Challenge) rules:
http://apolyton.net/forums/showthrea...threadid=22562
Zero Facilities Challenge rules are more difficult to find. Here's a description taken from version 4 of Vel's guide:
1) Only the Standard Map of Planet is allowed.
2) The following game settings must be adhered to
a) Transcend/Ironman
b) Rare Lifeforms
c) Blind Research
d) Tech Stag
e) Aggressive AI
f) No spoils of war
g) Do or Die
3) You are not allowed to build any base facilities. These base facilities are not inclusive of those that come along with faction inheritance, or those provided by Secret Projects.
4) You are allowed to keep those base facilities left over from enemy's cities conquered (there is no need to recycle them).
If you're interested in other challenges, Vel's guide has lots more.