Yes.
Although crossing back into the United States without a passport or WHTI compliant Drivers License (must denote citizenship, they are only currently offered by NY, WA and a couple of other states) means you are not in compliance with the new regulations as of now the only penalty is the possibility of a longer wait (at the border crossing in San Ysidro, CA you can expect to wait an additional 1-3 hours in the non WHTI compliant line while at Otay Mesa there would be no difference) however there are rumors that fines may soon be implemented for repeat offenders.
No and you need a passport as well.
No. NTSA guidelines require a passport (foreign or US), US passport card, green card or US drivers license or non-drivers license.
Yes
No. NTSA guidelines require a passport (foreign or US), US passport card, or US drivers license or non-drivers license.
No, you can't
Yes, but you must have an international drivers license or drivers license paired with passport and major credit card.
No
No
You need to be 18 to get you drivers license but when you are 16 you can drive with a guardian that has a drivers license.
No, you need a passport to enter another country.
No. NTSA guidelines require a passport (foreign or US), US passport card, or US drivers license or non-drivers license.
Short answer, none.
No. You can only get a California license if you're a resident of California.