How can Hussein be the master of the youth of the People of Paradise when he rebelled against Yazid, and can he be a master over a prophet who died young?

Al-Hasan and Al-Husayn are the masters of the youth of Paradise, but this does not give them preference over the prophets or the Rightly Guided Caliphs. The prophets hold the highest stations, by the consensus of scholars.

As for Al-Husayn’s challenging Yazid for leadership, this is not considered a flaw in him. Al-Husayn exercised ijtihad (independent reasoning) in that matter, and he saw himself as more deserving of leadership. He is excused and rewarded for his ijtihad. Al-Husayn retreated before the fighting when it became clear to him that the matter would lead to corruption, and he requested one of three things, but they insisted on humiliating him. A believer should think good of his noble predecessors.