How can the noble verse: "And when the Horn is blown, there will be no family ties among them that Day, nor will they ask about one another" be reconciled with the noble Hadith: "Every lineage and kinship will be cut off on the Day of Resurrection except my lineage and kinship"?

The reconciliation between the verse and the hadith is that the hadith specifies the general meaning of the verse. Kinship and lineage will be severed on the Day of Resurrection, except for the kinship of the Messenger of Allah, peace and blessings be upon him, and his lineage, in honor and exaltation of him. Many hadiths attest to this, including the Prophet's saying, "By Allah, my kinship is connected in this world and the Hereafter." The hadiths that urge his household to fear Allah do not contradict this; they mean that he himself does not possess any benefit for them, but Allah possesses their benefit through general and specific intercession. Thus, every kinship will be severed on the Day of Resurrection except for the kinship of the Messenger of Allah, peace and blessings be upon him.