Yes, but depending on your home country you would also need a visa issued by the Mexican government.
If you live in Mexico then no.
To fly into Mexico you HAVE to have a passport. As of right now the only way you can get into Mexico without a passport is by land travel, but that will change as of Summer 2009. As of Summer 2009 you will need a passport for any land travel into Mexico and Canada.
If you are traveling from outside Mexico, all cities you travel to require a passport.
nope
If you are planning travel to Mexico from South African, the passport holders do require a visa. Please contact your embassy for further details and all necessary forms to apply for the travel visa.
Yes
No. New Mexico is part of the United States, so you don't need a passport. :)
Yes you can, but you also need a visa if you try to enter Mexico with a South African passport. Greencards are not recognized as a traveling ID or document.
No. A passport is sufficient to travel to Mexico. A birth certificate is not valid for international travel. If you are traveling by land or sea, then you can enter Mexico with a US passport card, "enhanced" drivers license or "enhanced" non-driver ID.
To Canada you can; to Mexico you can't.
If entering Mexico via airplane, yes.
Yes.