If you are a resident of the US, you need a passport to travel to ANY other nation and to return to the US.
Yes, especially if you board a flight into Mexico. For land crossings, you would need an ID or birth certificate.
If you live in Mexico then no.
Yes
No. New Mexico is part of the United States, so you don't need a passport. :)
Yes, you always need a passport when you travel outside your country of origin.
No. Both are in the United States. You do not need a passport to travel from state to state.
Yes.
Yes, you do.
Yes, they do.
Yes you do
Yes
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.
No. American citizens don't require a visa to enter Mexico. All you need is your passport.