No, it's more that, Jesus religion is Judaic, yet not what is normally in arguments and such, the same as 'Judaism', meaning Rabbinical Judaism. The context is when the argument is made that these are just writings, not prophecy, so forth. More so, if said to be entirely made up, an academic claim, which we did encounter in the Messiah discussion.
I would say, yes.
I believe it's Acts of the Apostles, 'Jews from all over', and the inference is that there is variation. We get direct inference anyway, because of Essenes, Jesus's practice, so forth.
The Jewish Bible and the Xian Bible were canonized later, in fact book of Galatians seems to contradict a portion of Genesis 17, so there's that.