I would have to do some research to answer the rest of your questions, but with regards to this part -- "At what point did a majority of ethnic Jews convert?" -- the answer is, never. As far back as the Seleucid Empire's conquest of Judea, and especially once the Hasmoneans rebelled and founded their own dynasty, different sects of Judaism started diverging. A century or two later, when Judea was absorbed by Rome, there were quite a few sects around. Christianity was only one of those, but there are a few others you may have heard of -- the Essenes, who are usually credited with writing the Dead Sea Scrolls, for example.

Of those sects, the two that survived are the sect that would become Rabbinical (the modern form of) Judaism and Christianity. The reason that Christianity survived is because, unlike the other sects, it did not pull the majority of its adherents from the Jewish population. Instead, early on in its history, it started accepting (and proselytizing) pagan converts in large numbers.

So most early Christians, beyond the first few years, were not converted Jews -- they were converted pagans. Even without delving into its particular appeal to that population, this explains why it got so many adherents -- the Roman Empire had many more pagan citizens then Jewish ones.

You might ask over at a/r/AcademicBiblical as well.