U.S. citizens entering by car from Mexico are required to have their passports as well as other supporting documents. These include NEXUS, SENTRI and/or FAST.
Canadian, American and European citizens can enter Mexico without additional requirements other than their passports.
You only need a valid passport to enter Mexico.
To legalize a car from the U.S. for use in Mexico there are few forms to fill out and an approval is needed from customs. Also there may be varying fees for customs and for registration.
Having a passport and/or Visa is a legal way to enter the U.S. from Mexico.
No
Your birth certificate will not help you. You can enter the US from Mexico with an "enhanced" US drivers license, but only if you are traveling by sea or land, not by air.
As long as you have a US visa with you, you can also enter Mexico.
To gain Arizona and New Mexico from Mexico
Mexico
Yes. Also a US visa.
No. Having a visa for the US doesn't grant you the possibility to enter Mexico; you need the corresponding visa from Mexico.
They enter the us with green cards or by ridding in someones car, or truck.