There are way too many modeling agencies in California to name but many are legit, reputable and represent kids. A basic Google search will give you a list of the most notable agencies. Visit the official agency websites, which will contain all of the info you're looking for, including what types of models they represent.
Swish Model Management appears to be the most reputable modeling agency that is not a school.
Yes
Use a reputable one. get a recommendation from an agent not an agency
You must be signed to a reputable modeling agency that has JC Penny's as a client.
Two reputable modeling agencies are the kamera kids professional modeling and Carolyn's model and talent agency both located in Toronto. http://www.kamerakids.com/ http://www.carolynsonline.com/
Rosey's in Sydney is a well know and reputable agency that represents both models and actors.
Your child will have to be signed to a reputable and legit local modeling agency that has a children's division.
It is best to find a modeling agency in your town to represent you and find you legit and well paying work. Make sure the agency you send in your pictures and information to has a teen division.
wilhelmina Modeling Agency
If you are looking for a modeling agency, there is Bellissima International Model Management. Aside from signing with a modeling agency, you can do freelance modeling, which involves you acting as your own agent and finding your own modeling work, however, this option is not recommended for those that are not 18 years of age or older.
Nevs Modeling Agency is located in London.
The best way is to become a fashion/runway model that is signed to a legit and reputable modeling agency.