RECORDED STATEMENT: Should I give a Recorded Statement to the insurance Claims Adjuster in my California Personal Injury case?

No.  Unless, your case is so minor, that your car sustained virtually no property damage, or you treated once or twice with your doctor and you are okay medically speaking.  Outside of this, you should never give a recorded statement without the presence of legal counsel.  Most of the time, your statement will be used to minimize your injury claim.  Remember, the insurance companies are running a business (which means "for profit").  Thus, they do not want to have to pay out full value on a claim unless they are forced to take responsibility to do so.