After the legitimization of Christianity, it became equal to other religions. This happened in 313. CE by the adoption of the Milan Edict by Emperor Constantine. However, the Roman Empire fell later, after that. The Catholic Church continued to grow even after the fall of Rome, because it could, as such, be organized politically economically and socially. There was no state-level ban to prevent it. Many emperors of newly emerging states on the ground of the former Roman Empire, helped the Church, saw in it allies and support for political and economic goals. Christianity was for this purpose, proclaimed the religion of the masses, but also the Christianization was carried out as a way of conquering the so-called barbaric European tribes in order to obey them. When a religion is established at the state or empire level, it becomes a practice that is transmitted within the family to every next generation.
So, third, fourth and fifth answers are correct.
