explain the difference between the split that caused Judaism and Christianity to become separate religions and the split that caused Protestantism and Catholicism to become separate denominations

Christianity is rooted in Second Temple Judaism, but the two religions diverged in the first centuries of the Christian Era. Christianity emphasizes correct belief (or orthodoxy), focusing on the New Covenant as mediated through Jesus Christ, as recorded in the New Testament. Judaism places emphasis on correct conduct (or orthopraxy),focusing on the Mosaic covenant, as recorded in the Torah and Talmud.

Christians believe in individual salvation from sin through receiving Jesus Christ as their Lord (God) and savior. Jews believe in individual and collective participation in an eternal dialogue with God through tradition, rituals, prayers and ethical actions. Christianity generally believes in a Triune God, one person of whom became human. Judaism emphasizes the Oneness of God and rejects the Christian concept of God in human form.

Judaism's purpose is to carry out what it holds to be the covenant between God and the Jewish people. The Torah (lit. "teaching"), both written and oral, tells the story of this covenant, and provides Jews with the terms of the covenant. The Oral Torah is the primary guide for Jews to abide by these terms, as expressed in tractate Gittin 60b, "the Holy One, Blessed be He, did not make His covenant with Israel except by virtue of the Oral Law to help them learn how to live a holy life, and to bring holiness, peace and love into the world and into every part of life, so that life may be elevated to a high level of kedushah, originally through study and practice of the Torah, and since the destruction of the Second Temple, through prayer as expressed in tractate Sotah 49a "Since the destruction of the Temple, every day is more cursed than the preceding one; and the existence of the world is assured only by the kedusha...and the words spoken after the study of Torah."

According to Christian theologian Alister McGrath, the Jewish Christians affirmed every aspect of then contemporary Second Temple Judaism with the addition of the belief that Jesus was the messiah,[9] with Isaiah 49:6, "an explicit parallel to 42:6" quoted by Paul the Apostle in Acts 13:47 and reinterpreted by Justin Martyr. According to Christian writers, most notably Paul, the Bible teaches that people are, in their current state, sinful, and the New Testament reveals that Jesus is both the Son of man and the Son of God, united in the hypostatic union, God the Son, God made incarnate; that Jesus' death by crucifixion was a sacrifice to atone for all of humanity's sins, and that acceptance of Jesus as Savior and Lord saves one from Divine Judgment, giving Eternal life. Jesus is the mediator of the New Covenant. His famous Sermon on the Mount is considered by some Christian scholars[16] to be the proclamation of the New Covenant ethics, in contrast to the Mosaic Covenant of Moses from Mount Sinai.

Christianity- These groups all branched out at different dates from the early Christianity founded by the followers of Jesus. The splits generally happened because they could not agree on certain beliefs or practices. The groups then divided into smaller groups. Each group that has its own separate name is a "denomination".

Judaism - Judaism, monotheistic religion developed among the ancient Hebrews. Judaism is characterized by a belief in one transcendent God who revealed himself to Abraham, Moses, and the Hebrew prophets and by a religious life in accordance with Scriptures and rabbinic traditions.

Catholic and protestant war:

After the Protestant Reformation, these independent states became divided between Catholic and Protestant rulership, giving rise to conflict. The Peace of Augsburg (1555), signed by Charles V, Holy Roman Emperor, ended the war between German Lutherans and Catholics.

why did Protestanism break from catholism?

The Reformation began in 1517 when a German monk called Martin Luther protested about the Catholic Church. His followers became known as Protestants. Many people and governments adopted the new Protestant ideas, while others remained faithful to the Catholic Church. This led to a split in the Church.

Hope this helps :)

letter d is correct.

formulating the initial idea for the policy

answer is c.