You do if the immigration officers at passport control ask you to, but this isn’t particularly likely. Weasel McWeasel is right about the Permesso; however, you also need to know that you have 8 days to report your presence to the Questura in the town where you are staying when you enter Italy. Most tourists don’t have to worry about that because if you’re staying in a hotel, they make a copy of your passport and report to the police for you. This may be relevant in your case if you’re staying with your relatives rather than at a hotel.
If you are going for a visit………you have 90 days…….after that, you are in the country ILLEGALLY……….relatives or not. If you wish to stay, you will need to ask for a Permesso Di Soggiorno.
that is a TEMPORARY permit to allow you to stay, if you can prove you have a place to stay and a means of support. They do NOT *have* to grant it, and you can easily be DENIED, at their whim.
It is good for one year and will be need to be renewed—again, at their descretion to approve or deny for ANY reason they like. If you are here long enough,….you can then apply for Italian Citizenship, as I have done.
Absolutely not. VISITORS don’t have to show evidence they can sustain themselves. If you intend to move the Italy, any required paperwork should be done at the Italian Embassy in your country of origin before you arrive. In any case, the airport CAN’T handle the issue.