Yes, in general you can use your Mexican license as long as you do not become a resident of California:
If you are a visitor in California over 18 and have a valid driver license (DL) from your home state or country, you may drive in this state without getting a California DL as long as your home state DL remains valid.
If you become a California ...
According to TIMATIC, the database used by airlines to decide whether a passenger's documents are sufficient, you can indeed use a birth certificate to prove your US citizenship when arriving by air, but as noted in a comment, you will probably have to identify yourself with a photo ID before being allowed to board the plane in Mexico. The TIMATIC text:
No. As a US citizen, your son has visa-free access to Mexico for up to 180 days. See Visa policy of Mexico for more information.
If your son has any other citizenships (like Russian for example, but you didn't say either way), that doesn't matter if he enters Mexico using a US passport.
Realistically nobody can answer that question. Most people because they don't know the answer, and the people that do know the answer because they will not be allowed to share it!
The level of information sharing between countries is something that is not made public. There are absolutely agreements between specific countries to share information - with ...
Visas to enter Mexico, if you need one, are obtained before entering the country (eg from a consulate in your home country), so I gather you are actually referring to the FMM tourist permit (which is not a Visa). This permit just says you have been permitted to enter Mexico for the specified number of days.
Whenever we had them issued we had to fill in a ...
It seems that it is quite possible, as outlined in great detail here in this blog entry.
Buying a Used Car in Mexico as a Foreigner
Here is what we found out
straight away about buying a used car in Mexico: the only ones you’re
going to find for $1000 and under are mostly the old beat up VW bugs
you see everywhere. I’m not knocking it – I want ...