Thanks. My degree's in Latin, so I can only comment on early Christianity, although being Christian and a Roman History teacher, I've studied a lot of Early Christianity. But building on your comments:
Christians were socially persecuted in the early days, but the formal persecution did not start until fifty years after the last apostle died. Everything previous to that were murders by local bureaucracies, not a formal declaration of any belief being illegal. The Romans were both superstitious and henotheistic, meaning they had nothing against anyone worshipping whatever he wanted, but they recognized that various gods had the ability to hurt them, and invoking such was illegal. This is evidenced by the great number of rich and influential people, from Christ's time on, who were Christians. This may have been where the Christians first got in trouble--since they'd claim credit for every famine and plague.
At least as far as my readings and schooling went, there is no historic evidence, other than Catholic oral tradition, that Constantine became a Christian. Constantine presided over the Council of Nice, and defined the Trinity and made other such crucial decisions from that pulpit, dressed entirely in the garb of Sol Invictus, with full face-paint. At least as far as we have record, he made whatever decisions minimized conflict, and was a famous supporter of not persecuting Christians. But that doesn't mean he was a card-carrying church-member.
When the sabbath was changed from Saturday to Sunday is up for debate. I think most consider verses like Acts 20:7 as an evidence that the Saturday/Sunday transition was one of the many reversals that happened at the atonement.
I agree with everything else...
Anyone who wants to fiddle with this stuff, the best book, and the easiest, and a wonder Sunday afternoon read, is "The Rise of Christianity: How the Obscure, Marginal, Jesus Movement Became the Dominant Religious Force in the Western World in a few Centuries" by Rodney Stark. Go get it on Amazon (If I could link, I'd link you there). Stark is the big gun of religious sociology. I can recommend many others, but they're less academic, tougher to read, and more emotionally charged...