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.
Seems they are prepared for this. Someone I met had Thai handwriting on his visa, I didn’t.
Google translate showed the writing noted that passport expires before visa and to allow transfer.
They will be especially aware as dependents are part of the visa. Children are only issued 5 year passports (well in UK - I don’t know all countries!).