According to Wikipedia, a papal bull of 1058 In Nomine Domini reserved the right of election to cardinals only. The only non-Cardinals who have been elected to the Papacy would be:
Pope Celestine V
Pope Clement V
Pope Gregory X
Pope Urban IV
Pope Urban V
Pope Urban VI
Before that time there was not an established College of Cardinals as we understand them today, so more non-Cardinals were probably elected in the first millennium.
There have been a number of popes who were not cardinals. Pope Urban VI, pope from 1378 to 1389, was the last Pope to be elected from outside the College of Cardinals.
Popes are not appointed, they are elected and nearly all have been cardinals before becoming the pope.
Yes, there have been several popes that were related - one father and son and several popes had nephews who were elected as pope.
Cardinals are named by the pope; that's the only way, as far as I know. Currently, those cardinals that are younger than 80 years participate in the election of the pope. Thus, the electors of the next pope have been appointed by one of the previous popes.
The popes were chosen almost immediately after the death of the sitting pope. The earliest popes were chosen by consensus of the clergy and people of Rome. In 1059 it was ruled that the cardinals should elect the pope. In 1274 the Church ruled that the cardinals should be locked away (Latin: cum clave) until a new pope has been chosen. From that came the English word conclave.
For several centuries the pope has been elected from among the cardinals. It is not a requirement but has become a tradition.
He has never been married. Priests, including cardinals and popes.
There have been 15 popes named Benedict. Please be specific.
There have been three popes from Africa. All were from northern Africa.
Most, but not all, popes elected since 1378 have been Italian.
Pope Benedict XVI who resigned in 2013 and Pope Francis who was elected that year.
By Apostolic Succession. That is the laying down of hands at the ordination to bishop (the last 'step' of the threefold ordination). Then a bishop is created cardinal by the current pope. One of these cardinals is to be elected pope during the big meeting after the death of a pope. E.g. Cardinal Ratzinger had been elected as pope Benedict XIV.