Henry positioned himself as a sort of God-Emperor who could do whatever he wanted. Anyone who got too close to him was subject to his casual wrath. Anne was no saint, but she didn’t deserve to be killed.
Yes, but the Reformation was rather nationalist. The main argument, aside from theology, was that the marriage of an English monarch was an English concern. By not allowing the annulment of Henry’s marriage to Catherine of Aragon, the Catholic Church essentially had control over the succession, since Catherine was not able to have any more children except Mary.
Henry believed that a woman could not rule England, so he needed to remarry to have a son. Of course, both his daughters ruled, but he was going on English history at the time.