Its not always so black and white. In general, I agree that your son, and not you as the parents of a 20 year old, would be responsible for any injuries resulting from a fight. However, under some circumstances, you could be held responsible for damages. For example, if the incident took place at your home, i can think of some circumstances where you could also be held responsible. It is very fact specific and you haven't provided enough information.
The information provided herein is not intended to be legal advice, but is for information purposes only and is based on the limited information provided. Any information provided is not intended to, and does not, create any attorney/client relationship where none exists.
Not typically. If the fight occurred on your property or at event you were hosting there may be some potential liability dependent on the facts of the case. If your son's permanent residence if your home then he should be considered a resident insured and covered by your homeowner's insurance policy. So if he happen to get sued for personal injuries, depending on the nature of the claim, he may be covered. If he is used for an intentional act there will be no insurance coverage and he will have to pay for a lawyer to defend him.