What sort of legal implications or liabilities would someone take on by hosting this person? For example, if the child got hurt or in a bad accident, would they have the legal obligation to pay for him? And would this child fall under the hosts' medical insurance, or would he have to pay for his own medical insurance?
"Exchange student" programs have existed for long time. Usually the exchange students are required to buy at least "catastrophic" health insurance, and they might have to pay the tuition for the high-school they attend (even if it is a public school, since their parents are not us citizens and haven't been paying taxes).
The family is required to provide food, shelter, and some basic transportation, but that's it.
Students are required to have some money aside for monthly expenses.
I never have heard bad stories from the family side (i.e. they end up with a bad students) as the students themselves are well filtered. Most horror stories I have heard is from the students, where they go to a family and then they find themselves they have to babysit or do other stuff they are not expecting to.