Hi Chuck1,
The Popes role is to give guidance to and definition of, the Catholic faith. He is the supreme pastor of our Church. Only the Pope can call an ecumenical council, where Catholic doctrine is discussed, and only the Pope can confirm the decisions of such a council.
Through his speeches and writings, the Pope communicates understanding of the Catholic faith. The guidance and thoughts offered by the Pope help Catholic “live their faith” more truly, for their own benefit and that of the society they live in.
He is also the chief administrator of the Catholic Church and it is he who appoints Bishops and Cardinals (the latter group being those who will vote to elect his successor, amongst their other roles).
He also has a political role, as the head of a sovereign state, and so maintains political relations with secular Governments, including ones from non-Catholic nations (mostly recently malaysia
bbc.co.uk/news/world-asia-pacific-14181314)
Yes, the Pope is guided in his role by the Holy Spirit, as we all are when we pray and seek to know God.
Each Pope is the successor of the previous. You are right that they are not blood related, but it is the succession of the
position of Pope - and the Catholic unity and Papal authority he represents - which is traced back to St Peter, not a family bloodline. St Peter became the first Pope, and down the centuries there have been 264 more after him, including Pope Benedict XVI in the present day.
Cheers.