We will not know until the current pope dies and the Cardinals choose a new pope in a secret conclave.
Since Pope Francis is the first and only pope by that name, there is no need for a number after his name. If a pope in the future also decides to take the name Francis, he will become Pope Francis II and then the original Pope Francis will become Pope Francis I.
You may be referring to St. Malachy but he was a monk and not a pope.
A Pope has only once ever visited Ireland, in 1979. That was Pope John Paul II and he was made very welcome. Should any future visit by a Pope to Ireland happen, he would also be made welcome.
Pope Benedict is now retired - Pope Emeritus Benedict XVI - and has no involvement in the governing of the Church. He spends his time in prayer, meditation, reading and writing. If he is working on any future books, he has not released that information.
If you mean the Malachi Pope Prophesy, Benedict was the last Pope. Originally Malachi predicted only 111 future Popes. Benedict was the 111th. The 112th name on the list was added 400 years after the death of Malachi by a Benedictine monk that felt the Church should go 'out' on a more positive note. He added Peter the Roman, not Malachi. So, Peter the Roman is not a valid part of the Malachi predictions.
Pope Paul VI was elected pope after the death of Pope John XXIII.
John Paul II
There is no pope named Pope XXIII. If you are referring to Pope John XXIII, he became pope in 1958.
Pope Francis is the reigning pope in 2013.
The current pope is Pope Benedict XVI.
Pope Pius III was the predecessor of Pope Julius II.
Pope Benedict followed Pope John Paul II as pope.