Re: paperwork. I would have thought a signed letter from the parents stating their child is in your care and they give permission for you to make medical decisions on their behalf. Alongside photocopies of both parents & child’s passports also signed will be enough for all possible situations.
Make sure this teen has correct insurance and you having the details will be vital.
Maybe make sure parents tell insurance company that you are ‘in charge’ and to accept your calls etc.