How to refer to multiple members of a family?

This summer, I will be going to Nagoya for 3 weeks to stay with a family; however, I do not know how to refer to them by their last names without them getting confused. It doesn't seem logical to say "lastname"san and everyone turns their head thinking I was referring to them. Since I would be staying with them, would using their first names be acceptable? Everyone is younger than me except for the father and mother. I would like to be as respectful as possible without seeming like I'm trying to distance myself.
Also, any tips for when I visit a Japanese high-school? :)

If you're home-staying, the family will tell you what to call them, but most likely you'll call the dad otousan, the mom okaasan, and the kids by their names. If they have a different idea than that, they'll tell you.

At school, all the teachers are XX-sensei. For the kids, it might be easier to just stick to XX-san for now, but also as a foreigner, it's cool to just call them by name if you're unsure. And at that point the kids should know "call me xx" in English, so again, they'll probably tell you what to call them. So don't worry about it.

School's out during summer. What's the purpose of your stay? Student exchange or sightseeing? Who is this family to you? Relative, friend or host family? The answers depend on those situations.

Well I will be visiting the highschool for a week or two before they are totally out. The family themselves are a host family, but it is a unique situation. They are a friend of a mutual friend. I do speak a little Japanese so that's why I want to make sure I can decently fulfill any expectations that they may have
By the way, thanks for your help guys

Thanks for the follow-up. I assume you're a high-teen. If not, please say so, because it also differs depending on the age range.

Well, the safest way is to ask how they want you to call them. That said, when speaking in Japanese, Japanese teens typically call families as follows:

The father: ojisan
The mother: obasan
Their children: (first names)

Also, suppose you are the family son's friend, and that the son's name is Taro. You can also call them like this:

Taro: Taro-kun
Taro's father: Taro-kun no otousan
Taro's mother: Taro-kun no okaasan

If Taro is older than you, you should call him "Taro-san".

But when speaking in Japanese, you can usually get away without addressing the other party at all. But if you are indeed calling them, it would make a great impression if you always put -san at the end.

As for school, I'm sure you will be visiting it with someone who will guide you. So just listen to whatever that person tells you. You will typically change to slippers (which can be provided by the school) inside the buildings. Typically, you need to visit the teachers' office before entering the school premises. Try to use keigo to the teachers if you can.

Hope you have fun!