Q. 1. Do you know the mailing address of the Pope?

A. 1. The website for the US Embassy to the Holy See recommends that mail for Pope Francis be sent to this address:

His Holiness, Pope Francis
Apostolic Palace
00120 Vatican City

"Italy" and "Rome" are not a part of the address since Vatican City is a country of its own.

Since, unlike previous popes, Pope Francis is living in Casa Santa Martha instead of the papal apartment, another address you can try is this:

His Holiness, Pope Francis
Saint Martha House
00120 Citta del Vaticano, Vatican City

In both situations, please make sure that you have the correct postage. If you are unsure of what you need, ask your local post office.