OK. Once more...
A moped or motorized bicycle is any bicycle with a motor attached, that has a displacement of 50CC or less, 2HP max, has an automatic transmission and pedals for human propulsion.
You must wear a helmet as it is a motor vehicle. The 18 and over law is for BICYCLE riders.
You must register it with the famous motorized bicycle plate for six bucks.
You need to have the minimum of a car drivers license or learners permit. you can ride a moped in a Class2 bicycle lane, which is a lane on the right side of a roadway marked off for bicycles. You cannot operate a moped on a Class 1 bikeway, which is a dedicated roadway for bicycles and pedestrians.
You do need insurance, but the law is not too clear on it.
Don't rely on a sellers' statements when interpreting the law. The judge won't accept "But the seller told me that..."
Get caught without a helmet on a motorized bicycle, motor-driven cycle, or motorcycle in the Golden State and it's a 200 buck fine.
I reasearched all this stuff myself when i couldn't get a straight answer from the DoDoes at DMV.