What will happen to you and your learner's permit due to this accident and the restrictions or laws that you were not following will be determined by the DMV or courts (depending on if you were cited). As for damages from the accident, since you were not at-fault you, or the owner of the vehicle you were driving, should be able to make a claim against the at-fault party's insurance policy.
If you are under 18 years of age, it would appear that during the time of your accident you were not complying with the passenger rule of the learner's permit or the financial responsibility (FR) law. It could be possible that while you do not have insurance under your name, if your parent's insurance company was aware of your permit and was covering you while driving then the FR law might not be a problem.
Typically, California's compulsory financial responsibility (FR) law requires every driver and owner of a motor vehicle to maintain financial responsibility at all times. If you are under 18 years of age, your parents sign your license application and assume financial responsibility for your driving though.
In California if you have a permit and have one at-fault accident within 12 months you will get a warning letter from the DMV. If you are involved in a second at-fault collision within 12 months, you will not be allowed to drive for 30 days. Because you were not at-fault these penalties should not apply to you.
As for the exact penalties you will receive, you will have to find these out from the CA DMV. The DMV or court determines what actions are taken against permit holders that do not follow the restrictions. Since you were not at-fault in the accident it could help your case.