Short answers, pulled from the story.
The Acts of Supremacy established the English monarch as the head of the Church of England, replacing the authority of the Pope. The first act in 1534 declared Henry VIII the Supreme Head of the Church; the second in 1558 declared Elizabeth I the Supreme Governor, a title the British monarch still holds.
Henry VIII passed the Act of Supremacy 1534 primarily because Pope Clement VII refused to annul his marriage to Catherine of Aragon. Henry wanted a male heir and had convinced himself that God was punishing him for marrying his brother's widow; the Pope's refusal, partly influenced by Catherine's nephew Charles V, left Henry no path forward within the Catholic Church.
Henry VIII's Act of Supremacy was repealed in 1554 during the reign of his Catholic daughter Mary I. When Mary died in November 1558, her Protestant half-sister Elizabeth I restored royal supremacy over the Church through a new Act of Supremacy passed in 1558.
Henry VIII's 1534 act used the title Supreme Head; Elizabeth I's 1558 act used the title Supreme Governor instead. The change was intended to pacify Catholics and Protestants who were uneasy about a woman claiming full headship of the Church, while still asserting royal authority over church and state.
Thomas More was the most famous public figure to resist the Treasons Act 1534, which made it a capital crime to deny the king's title as supreme head. More was convicted of treason and executed by beheading.
Yes. The Parliament of Ireland passed a parallel act in 1537 establishing Henry VIII as supreme head of the Church of Ireland, and a further act in 1560 restoring Elizabeth I's supremacy over the Irish church. The 1537 Irish act remained partially unrepealed until the Statute Law Revision Act 1950 struck it from Northern Irish law.