Can I camp on a campsite under 18 in Italy?

Campsites if you're under 18: It's difficult to find information on campgrounds that allow you to stay if you're under 18. As far as I know, there isn't a website that specifically lets you search for hostels that allow minors. But one starting point you can try is https://www.pitchup.com by doing a search and then choosing to filter by "student groups welcome". That's not quite the same thing, but it's a good way to narrow down your list to the ones that are much more likely to be ok with you staying there. But you'll still need to contact the campground first to be sure.

Hostels if you're under 18: Since you mentioned that you were first thinking about hostels, a lot of hostels do let you stay if you're under 18. To see a list of hostels that let you stay if you're under 18, you can go to https://www.hostelz.com, search for the city you want, then click the "Suitable For" drop down menu and choose "Underage without Guardian". As far as I know, this is the only website that has a search filter to find hostels that allow minors.

[Disclaimer: I helped create Hostelz.com.]