Is the supplication of a person from the Prophet's Household (Ahl al-Bayt) different from the supplication of a person from another lineage, and will all lineages in this world perish, with only the lineage of the Prophet's Household remaining?

The general texts indicate no difference between a supplicant from the Prophet's household (Ahl al-Bayt) and others. Supplication is an act of worship required from everyone and is promised a response. Allah Almighty says: (And your Lord said: "Call upon Me; I will respond to you." Indeed, those who disdain My worship will enter Hell [rendered] contemptible.) Supplication is always required with persistence and without haste, as stated in the Hadith: (The supplication of anyone of you is granted as long as he does not show impatience by saying, 'I supplicated but I was not granted my supplication.') As for the severance of lineages mentioned, it refers to the Day of Resurrection, when no one will benefit another, except the lineage of the Prophet, peace and blessings be upon him, if the Hadith reported concerning it is authentic.