If these convictions were in juvenile court when you were a minor go back to court and get the records sealed. This does not happen automatically. In California employers can only ask about convictions. It appears that you were convicted (a no contest plea has the same effect as a guilty plea). You are not required to reveal arrests and once your records are sealed will not have to disclose those either.
Mr. Driessen is a former Deputy DA in Orange County with over 8 years of criminal law experience. Nothing stated on this site shall in anyway be construed as legal advice, or as creating any attorney client relationship. If you would like to hire Mr. Driessen, feel free to contact him at www.theocduiguy.com.
I would need more information to answer your questions properly. You say you were arrested and charged but not whether you were convicted. Additionally, it would depend on the questions you were asked in an employment application. Most applications ask for convictions only, not arrests. Also, most applications specify adult convictions.
My advice is to see a lawyer in your area and get advice. Also I would suggest sealing your juvenile record. It is relatively simple.
There are a few ways to allow you to answer "no" to conviction questions on job applications. Depending on what you plead to, and how long ago it was - this could be fixable. It may require a lawyer writing a motion, and you providing some materials to the judge, but it may be possible.
It's not something that you should try to do on your own though. A criminal defense lawyer could help you prepare the necessary papers.