What was the role of religion and the Church during the Middle Ages? How was that different from Ancient Rome or modern America? Explain.

This is a big question, but in broad strokes we can outline the chief differences.
Ancient Rome embraced religious pluralism for most of its history, though it did, in its last years, adopt Christianity as the official state religion. However, through most of its history, it allowed many different religious groups to flourish as long as those groups were willing to worship the Roman emperor (once Rome became an empire) in their pantheon of gods. Rome's biggest collusions came with Judaism and Christianity, because both of those religions were exclusivist: they only worshipped one god and refused to worship the emperor.
During the Middle Ages, in contrast to Ancient Rome, there was only one church, the Christian Church, although it was split into two parts, Roman Catholic and Orthodox Catholic. Religious pluralism was forbidden and non-Christians were stamped out. Christianity was a unifying force across Europe, and the pope had a great deal of influence on political affairs. Rulers were expected to be Christians and to have the approval of the pope. There was no separation of church and state.
Modern America, meaning the United States, has enshrined religious freedom and the separation of church and state in its Constitution. Like the Ancient Romans, we accept many religions and leave people alone to belong to whatever faith they wish as long as they obey the law.