Write down your plan with clear steps for your freelancing career,along with how long will it take to show genuine results. Additionally write your plan B incase it just doesnot work. Showcase it to your parents and i guess they will only support your decision. Currently they are saying no because this career is new to them and they are worried for you. Show them your plan and they will definitely support you. Best wishes for your freelancing career.
Additional advice: please dont lie to them. Just be open to them and see how they only help you.
Depends on the choice of work. If you're earning much out of freelancing, parents won't mind. Just convince them that this could also be a permanent source of income as they mostly worry about the stability of what we do.