You need a headlight with high and low beam and a taillight with running light and brake light. You do not need turn signals. Use hand signals instead.
Link to plate: http://www.dmv.ca.gov/forms/reg/reg230.htm
Chinagirls do not have engine numbers. Some however do have date of manufacturer numbers though. You cannot use this as a identification number though as there will be 100 or so engines out there with the identical number on them.
Most folks use the bicycle's identification number only with an "E" placed in front of it as the engine number.
You have to realize that in China these engines are seen as a utility device, like a shovel or a laundry basket. Why put a number on those?