Is it mandatory to add a 19 year old to my car insurance policy if he doesn't live with me?
If he is a member of your household or if he drives your vehicle then yes he must be added to your insurance policy. A member of your household includes students away at college. A student at college does not count as not living with you because their residence is still your house.
Certain forms of business insurance are mandatory and required by law. One example is worker's compensation insurance which must be carried by all businesses in all states. Other forms such as disability insurance are not required in all states so it varies by what state you live in. Most other forms of business insurance are not mandatory but are highly recommended.