Furthermore, how long did it take for Christians to outnumber Jews?
To understand early Christianity before the first council of Nicea, is difficult, the religion was heavily persecuted by the romans. Tacitus, writes in his final work Annals, "Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilate, and a most mischievous superstition, thus checked for the moment, again broke out not only in Judaea, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their center and become popular." Check that out here, persecution lead to the religion being heavily decentralized. In roman legal terms during the first century of Christianity's existence it was already a distinct religion. Judaism was legal in the empire while Christianity was an illegal religion. Eventually in 96 C.E. the Christians were truest separate as they no longer had to pay the Jewish religious tax. It was not till 313 C.E with the Edict of Milan, that Christianity was fully legalized. The edict states, "Therefore, your Worship should know that it has pleased us to remove all conditions whatsoever, which were in the rescripts formerly given to you officially, concerning the Christians and now any one of these who wishes to observe Christian religion may do so freely and openly, without molestation." (Check out the full text here.) For the separation of Christianity from Judaism in the eyes of Jews, the best case here may be The Council of Jerusalem in 50 C.E. The topic of the council, was circumcision of newly converted men, the council came to the conclusion that men were not required to be circumcised, meanwhile Jewish society still required men to be circumcised or they were seen as impure. (You can checkout the Vatican's article on the council here.) There were other occasions where splits became even more present but I'll neglect these to save time, because they would require me going into detail of the factional situation within the Jewish faith before the destruction of the second temple, the emergence of Rabbinic, and the great revolt. There is also the Council of Jamnia, though the validity of the existence of the council is somewhat disputed. There's a great article about the council, its validity, and what the council was about here. Judaism and Christianity's split took a while too manifest completely, by 313 C.E however it was undeniably separate at least in roman legal terms. However as christians did not have to pay the tax Jews did they were technically already seen as a legally distinct entity. Meanwhile the Christian split from mainstream Judaism, occurred around the time of the Bar Khobba revolt, which I neglected due to the extremely complicated nature of the topic. I'd recommend googling the topic and searching for documentaries as those will dedicate 45 minutes at least to the subject, and go into far more detail than I can. I digress however, by 132 C.E. Christianity was undeniably separate from Judaism. For more information on early Christianity, I'd check out extra credits's wonderful video series, on the subject, check the playlist out here.