Answer:
imma help u bro
question 1 - the colosseum, the Wall of Trajan, and the Aeineid
question 2 - the messiah was the prophesized saviour of all Jews, and so you can see why the Jews thought the messiah was important
question 3 - roman emperors persecuted christians mainly for their faith and belief in Christ, as they originally thought that Christ, an original Jew, illegally gave himself the title of messiah, and that he apparently called himself 'The King Of Jews', which, of course, was not the case.
question 4 - as the heir to the roman throne was emperor Constantine, who was secretly a devout christian at heart, and had belief in the faith and in Christ. He changed the roman empire to a christian one, and got everyone in the empire to believe in Christ.
question 5 - this question is actually wrong, as it was not the eastern roman empire to fall, but the western roman empire, and the eastern roman empire would then go on to be the byzantine empire. however, getting back to the question, the eastern roman empire survived longer as it had a number of advantages, the most prominent of which was the lack of germanic migration into eastern territories.