Catholics: What do the apostolic fathers mean by offerings for the dead?

Question

"As often as the anniversary comes round, we make offerings for the dead as birthday honours." Tertullian, The Crown, 3 (A.D. 211).

"Nor is that kind of title to glories in the case of Celerinus, our beloved, an unfamiliar and novel thing. He is advancing in the footsteps of his kindred; he rivals his parents and relations in equal honours of divine condescension. His grandmother, Celerina, was some time since crowned with martyrdom. Moreover, his paternal and maternal uncles, Laurentius and Egnatius, who themselves also were once warring in the camps of the world, but were true and spiritual soldiers of God, casting down the devil by the confession of Christ, merited palms and crowns from the Lord by their illustrious passion. We always offer sacrifices for them, as you remember, as often as we celebrate the passions and days of the martyrs in the annual commemoration. Nor could he, therefore, be degenerate and inferior whom this family dignity and a generous nobility provoked, by

domestic examples of virtue and faith. But if in a worldly family it is a matter of heraldry and of praise to be a patrician, of bow much greater praise and honour is it to become of noble rank in the celestial heraldry! I cannot tell whom I should call more blessed,--whether those ancestors, for a posterity so illustrious, or him, for an origin so glorious. So equally between them does the divine condescension flow, and pass to and fro, that, just as the dignity of their offspring brightens their crown, so the sublimity of his ancestry illuminates his glory." Cyprian, To Clergy and People, Epistle 33(39):3 (A.D. 250).

Answer 1

It refers to prayers and acts of self-sacrifice which we on earth offer to God on behalf of the souls in Purgatory, a belief of the original Christian Church, as your quote so clearly illustrates. This is what is referred to as "the communion of saints" in the Apostles' Creed. We continue to pray and offer personal sacrifices for these dearly departed today. One of the great tragedies resulting from the false doctrines of Protestantism is their failure to pray for their deceased friends and family.
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Answer 2

"In symbolic language, the Book of Revelation tells of this persecution by Rome (called Babylon). The Christian writer, Tertullian, later observed "the blood of the martyrs is the seed of the Church," and Christianity continued to grow by its witness of faith and courage. Christain bishops, the leaders of the church after the death of the apostles, continued to be models of faith for God's ppl - such as the bishops of Rome after Peter: Linus, Anacletus, and Clement.
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The relative peace of the third century mad many Christains grow comfortable and lax. The Church was shocked when Emperor Decius, fearing the growning number of Christains, called for the first empirewide persecution of the Church in A.D. 250. Christains who refused to offer sacrifice to the gods before special commissioners were imprisoned or put to death. Thousands of Christains renounced the faith ("apostatized") in the face of death, though some were martyred. The persecution ended as suddenly as it had begun in A.D. 251, and a dispute arose about whether those who had denied their Christna faith could be readmitted to the Church. Bishops Cornelius of Rome and Cyprian of Carthage taught that bishops could grant God's forgivness even for serious sins, like apostasy, though penances were long and severe."

Answer 3

In dieing we are born to eternal life. This is in regards to the feasts of Saints. The Mass's held in their honor where it is a great Heavenly banquet where we, the ones on Earth are drawn up to be with the Lord during these banquets. This is the true Rapture.

Answer 4

The answer is in the number 42.

Answer 5

You can read more on votive offerings here.