The Pope is the head of the Catholic Church, whose seat can be found in Rome. The "pope" word came from the Greek "pappas", which means father. Until the 4th century, all of the bishops had this name. After the schism, the name of the head of the Orthodox Church became "patriarch", so now just the head of the Roman Church has that name.

The Pope has a primal, absolute and direct authority in the whole Catholic Church. There is not appeal against his verdict. He gets his authority when he accepts his position. The Pope can wield his authority through the papal offices and courts. So when he dies, all of the officials lose their charges.

The 1st Synod of Vatican (1870) said , that the Pope is unerring by the clemency of the God, when he declares about faith and morality, united with all of the Catholic bishops, with pretence of infallibility (ex cathedra Petri) . The Pope uses this authority rarely.

PopePius IX on 8th of December in 1854 (Ineffabilis Deus: Saint Mary's undefiled conception)
Pope Pius XII on 1st of November in 1950 (Munificentissimus Deus: Saint Mary' ascension)
Pope John Paul II on 25th of March in 1995 (Evangelium Vitae: Abortion and mercy killing is sin.)

The cardinals have right to attend the Pope elections in the Catholic Church, they help the Pope, and give him advice. Their name "cardinals" comes from the Latin "cardo" word which means 'hinge', because they are necessary like the hinge, because the door can't work without it.
Their official titles: Sanctae Romae Ecclesiae Cardinalis, which means: Cardinal of the Saint Roman Church.

Every cardinal has a church, but there they haven't got rights. The Pope appoints them and now just a priest can be a cardinal, if he isn't a bishop, he will be appointed. There are places where a bishop or an archbishop also will be appointed to be a cardinal, but it isn't automatic.
A bishop gets his rights and obligations immediately after he becomes appointed, but there are "in pectore" cardinals whose name isn't public. As long as his name isn't public, he can't use his rights, and does not have obligations. This is applied in those countries, where a bishop will be in danger if everybody knows his name.
The bishops can't use their authority on the cardinals. The cardinals can shrive everywhere in the world, and the local bishop can't forbid it to them. Just the Pope can sit in judgment on them, and they can choose the place where the questioning is.